WEBVTT 00:00:05.000 --> 00:00:09.480 Right this now we're solving a quadratic 00:00:11.920 --> 00:00:14.260 Equation by factoring 00:00:17.300 --> 00:00:21.580 How do we so what's the first step we always do 00:00:24.840 --> 00:00:25.380 No 00:00:29.300 --> 00:00:32.360 Well before we do any of that, okay 00:00:32.940 --> 00:00:33.520 Oh 00:00:34.740 --> 00:00:49.980 We have to have a zero on one side, so what do I do subtract the 25? Yes 00:00:49.980 --> 00:00:51.900 Now what 00:00:55.840 --> 00:00:56.280 Oh 00:01:00.400 --> 00:01:03.060 Well in order to factor this what do we do first 00:01:08.200 --> 00:01:10.140 Multiply this out 00:01:10.140 --> 00:01:11.520 Oh 00:01:19.820 --> 00:01:21.860 And we got to distribute some stuff 00:01:40.160 --> 00:01:40.680 I 00:01:42.320 --> 00:01:43.660 Was that my 16 00:01:47.040 --> 00:01:47.560 Okay 00:01:48.420 --> 00:01:54.032 Yeah, we got to get zero to one on one of the two sides and then we got to put it in 00:01:54.032 --> 00:01:54.900 standard form 00:01:55.720 --> 00:01:57.020 standard form is 00:01:57.680 --> 00:01:59.500 some number of times x squared 00:02:00.260 --> 00:02:02.820 Plus the linear term plus the constant term 00:02:04.640 --> 00:02:06.840 We'll talk about that 00:02:07.640 --> 00:02:11.380 Now what? Now we have to factor. 00:02:13.340 --> 00:02:15.560 Got it, right 00:02:18.460 --> 00:02:23.040 What is it x plus 2 00:02:28.740 --> 00:02:31.000 And then what do we use 00:02:33.620 --> 00:02:35.880 Zero product property 00:02:36.800 --> 00:02:39.240 We have a product that equals zero 00:02:39.800 --> 00:02:42.520 Either x minus eight equals zero, or 00:02:43.300 --> 00:02:48.120 x plus 2 equals zero and now we no longer have a 00:02:48.940 --> 00:02:52.640 Quadratic equation we have two linear equations 00:02:53.640 --> 00:02:56.220 Thanks to the zero product property 00:02:59.300 --> 00:03:03.980 We got our two solutions 00:03:09.080 --> 00:03:14.865 This makes sense we did this last week the only thing we probably didn't do yeah was 00:03:14.865 --> 00:03:16.380 multiply something out 00:03:22.160 --> 00:03:25.480 That's solving by factoring: get everything to one side. 00:03:27.420 --> 00:03:29.840 Make sure zero is on the other side really 00:03:30.920 --> 00:03:34.840 Then we put in a standard form we factor it use zero product property and so on 00:03:35.740 --> 00:03:37.140 All right. Next question 00:03:56.880 --> 00:03:57.480 So 00:04:00.080 --> 00:04:04.000 By factoring we would get this to this side, right? 00:04:05.900 --> 00:04:07.920 And then how do we factor that 00:04:08.900 --> 00:04:09.720 Oh 00:04:09.720 --> 00:04:16.256 Difference of squares, okay. However, this is missing the linear term, right? So 00:04:16.256 --> 00:04:18.380 which property can we use? 00:04:20.640 --> 00:04:22.900 The SRP which stands for 00:04:23.900 --> 00:04:25.900 Square root principle. 00:04:27.860 --> 00:04:28.560 Square root. 00:04:30.440 --> 00:04:31.500 Principle. 00:04:36.100 --> 00:04:40.800 You equals plus or minus the square root of 25 00:04:44.980 --> 00:04:49.640 You equals plus or minus 5 00:04:57.220 --> 00:05:03.780 Which is two equations and we got our two solutions, right? 00:05:08.640 --> 00:05:11.300 Five and negative five, but I'm gonna go back for a sec 00:05:17.860 --> 00:05:19.580 When can we use the square root principle? 00:05:24.120 --> 00:05:25.400 When there's no what 00:05:26.260 --> 00:05:27.600 Linear term 00:05:28.300 --> 00:05:30.360 sometimes we call the coefficient of the 00:05:30.360 --> 00:05:36.040 Quadratic term we call it a the coefficient of the linear term 00:05:36.040 --> 00:05:41.734 We call it b, and the constant term we call c. Whenever b is zero, we can use the 00:05:41.734 --> 00:05:43.280 square root principle. 00:05:43.280 --> 00:05:46.320 What I failed to tell you was 00:05:47.960 --> 00:05:52.400 You actually equals X minus 3 00:05:56.500 --> 00:05:57.340 Okay 00:05:59.620 --> 00:06:00.460 Okay 00:06:01.020 --> 00:06:08.060 Okay, so we got X minus 3 squared equals 25 00:06:13.320 --> 00:06:15.980 Can we still use the square root principle 00:06:19.280 --> 00:06:20.960 We use it right here 00:06:22.680 --> 00:06:31.580 Here, x minus three equals plus or minus the square root of twenty-five. 00:06:36.220 --> 00:06:40.080 X minus 3 is plus or minus 5 00:06:42.440 --> 00:06:46.540 X is 3 plus or minus 5 00:06:46.540 --> 00:06:53.380 X equals 3 plus 5 or X equals 3 minus 5 00:06:53.380 --> 00:06:58.872 Okay, that's a great question why did we not do that right here one is got told you 00:06:58.872 --> 00:07:00.460 just solved by factoring 00:07:02.160 --> 00:07:04.540 Two is the whole point is 00:07:05.840 --> 00:07:09.900 To show us even though this is not X squared equals the number 00:07:10.920 --> 00:07:12.280 This is something 00:07:12.980 --> 00:07:14.160 squared equals a number 00:07:16.240 --> 00:07:18.160 Okay, let's call this 00:07:19.260 --> 00:07:25.446 You for a second we got u squared equals 25 we could still use the square root 00:07:25.446 --> 00:07:26.160 principle 00:07:28.220 --> 00:07:30.460 Okay, whatever is squared 00:07:35.200 --> 00:07:42.300 Whatever is squared this case is not just X it's X minus 3 we simply go X minus 3 00:07:42.940 --> 00:07:48.057 Equals plus or minus the square root of the other side and that is using the square 00:07:48.057 --> 00:07:48.920 root principle 00:07:51.280 --> 00:07:51.840 Okay 00:07:54.880 --> 00:07:56.320 Go with me for a second 00:07:57.180 --> 00:07:57.740 Okay 00:07:58.440 --> 00:08:02.300 It saves us a lot of time. We don't have to multiply out 00:08:02.980 --> 00:08:05.740 and bring everything over and then 00:08:05.740 --> 00:08:07.300 factor again 00:08:08.700 --> 00:08:11.220 Okay, so let me do another example 00:08:11.220 --> 00:08:11.740 We 00:08:11.740 --> 00:08:16.760 Have something squared equals a number 00:08:18.580 --> 00:08:20.520 Can we use the square root principle 00:08:22.620 --> 00:08:25.440 Yeah, whatever is squared let me call it you for a second 00:08:27.000 --> 00:08:31.720 X plus five equals plus or minus the square root of nine. 00:08:35.220 --> 00:08:39.260 X plus five equals plus or minus three. 00:08:41.800 --> 00:08:44.920 X equals five plus or minus three. 00:08:46.680 --> 00:08:51.060 Which is X two different equations 00:08:56.920 --> 00:08:58.480 We get 8 00:09:00.440 --> 00:09:01.040 2 00:09:04.040 --> 00:09:08.680 Negative five! Yes, thank you. 00:09:13.240 --> 00:09:19.460 Negative 2 and X equals negative 8 we got our two solutions 00:09:20.880 --> 00:09:21.840 Oops 00:09:31.720 --> 00:09:35.620 Okay, so we could use the square root principle 00:09:37.160 --> 00:09:40.720 When anything squared equals a number 00:09:41.820 --> 00:09:42.920 whatever squared 00:09:44.120 --> 00:09:49.320 Equals plus and minus the square root of the other side, which is two separate 00:09:49.320 --> 00:09:51.920 equations, and then we we go from there 00:09:51.920 --> 00:09:56.776 We're gonna solve this by well, we're sorry this can easily be solved by factor, 00:09:56.776 --> 00:09:57.140 right? 00:10:00.340 --> 00:10:02.140 Okay, what's this factor to 00:10:08.180 --> 00:10:10.320 Actually, let me do a different example 00:10:16.720 --> 00:10:24.280 This equals x plus five times x plus one. Then what do we do? 00:10:27.820 --> 00:10:31.020 Zero product property X plus 5 00:10:32.320 --> 00:10:34.400 X plus 1 00:10:43.500 --> 00:10:51.420 Actually, let me do a different problem 00:10:55.320 --> 00:11:01.320 Now let's do with this sorry, okay, let's take the same equation 00:11:10.140 --> 00:11:10.700 I 00:11:13.340 --> 00:11:15.400 Put this on this side 00:11:27.340 --> 00:11:29.880 I'm going to add something to both sides 00:11:33.780 --> 00:11:40.120 Okay, so when this factors it's a perfect square 00:11:51.020 --> 00:11:54.020 So I'm gonna add some number 00:11:56.200 --> 00:12:01.120 So it will factor to the same exact two binomials 00:12:03.200 --> 00:12:08.400 This gives a perfect square. What do you think we should add? 00:12:11.460 --> 00:12:13.480 Okay, she's saying add 9 00:12:22.020 --> 00:12:28.120 If you add 9 we'll talk about a second how we do that what is this factor to 00:12:29.100 --> 00:12:30.900 X plus 3 X plus 3 00:12:32.260 --> 00:12:33.700 X plus 3 00:12:34.420 --> 00:12:37.440 Okay, we'll come back this minute. Let's just finish this 00:12:47.080 --> 00:12:49.180 And once we're here 00:12:50.060 --> 00:12:55.440 What can we use now? What's something squared equals number square root principle? 00:12:55.720 --> 00:12:59.980 We get X plus 3 is plus or minus the square root of 4 00:13:07.420 --> 00:13:09.760 Which is two equations 00:13:21.260 --> 00:13:25.080 There are two same two solutions we solved by factoring earlier ago 00:13:29.480 --> 00:13:32.200 Once we write our two binomials 00:13:34.260 --> 00:13:35.840 These two 00:13:37.240 --> 00:13:39.300 Have to multiply to be this 00:13:42.020 --> 00:13:43.140 And then 00:13:44.820 --> 00:13:50.800 These two 3x and 3x have to add to be 6x 00:13:52.920 --> 00:13:53.600 Okay 00:13:55.680 --> 00:14:02.470 So we literally just take this B value divide by 2 and that's going to be the number 00:14:02.470 --> 00:14:03.440 here in here 00:14:06.440 --> 00:14:09.500 Okay, when we factor it which is B over 2 00:14:12.760 --> 00:14:13.800 And then 00:14:17.760 --> 00:14:21.020 To figure out what number we add we just take B over 00:14:22.140 --> 00:14:27.720 2 and we square it and that's the number we add so 6 over 2 00:14:28.820 --> 00:14:34.420 Squared this 3 squared is 9 and that's what we add to both sides of the equation 00:14:36.980 --> 00:14:40.400 Okay, this is called solving 00:14:44.080 --> 00:14:45.600 By completing 00:14:49.220 --> 00:14:50.540 The square 00:14:53.200 --> 00:15:00.560 Okay, why is it called solving by completing this square because once we're here 00:15:02.980 --> 00:15:09.524 We have to make we have to add something to make it a perfect square so we need to 00:15:09.524 --> 00:15:11.360 complete the square and 00:15:11.360 --> 00:15:14.300 That's we always add B over 2 squared 00:15:15.080 --> 00:15:19.760 And we got this we now completed this square. It's a perfect square when it factors 00:15:19.760 --> 00:15:22.520 It's gonna be something square a binomial squared 00:15:25.420 --> 00:15:28.600 Okay, let's try another one 00:15:28.600 --> 00:15:30.600 Here's a quadratic 00:15:34.280 --> 00:15:37.220 Polynomial that does not factor 00:15:39.420 --> 00:15:40.140 Okay 00:15:42.040 --> 00:15:44.980 Well, it actually does we'll talk about that in a second 00:15:46.700 --> 00:15:49.320 But the only options we know of our what? 00:15:50.960 --> 00:15:53.120 Negative 5 and 1 or 00:15:53.120 --> 00:15:57.220 five and negative one, and neither pair adds to eight. 00:15:58.020 --> 00:16:00.160 We agree. Yes. Okay 00:16:01.400 --> 00:16:04.420 So this cannot be solved by factoring 00:16:06.280 --> 00:16:12.080 The only other way we know of is by completing the square so the first step 00:16:16.880 --> 00:16:23.160 We get the constant term on the right the quadratic and the linear on the left 00:16:26.500 --> 00:16:28.380 And now we got to add something 00:16:32.840 --> 00:16:34.680 So becomes a perfect square 00:16:37.280 --> 00:16:40.700 You got to complete the square, so what am I gonna add? 00:16:42.350 --> 00:16:44.890 These two numbers have to add to eight. 00:16:46.690 --> 00:16:47.830 So which is 00:16:49.370 --> 00:16:51.190 8 over 2 is 00:16:52.270 --> 00:16:55.210 4 so it's plus 4 plus 4 00:16:56.110 --> 00:17:00.790 And then to figure out they have to multiply to be this number so we square 00:17:02.530 --> 00:17:03.130 16 00:17:04.770 --> 00:17:08.390 We add sixteen to both sides. 00:17:21.070 --> 00:17:25.470 And now we have something squared equals a number. What can we use? 00:17:26.710 --> 00:17:28.430 Square root principle 00:17:31.310 --> 00:17:35.990 X plus four equals plus or minus the square root of twenty-one. 00:17:36.990 --> 00:17:40.750 Does the square root of twenty-one simplify? No. 00:17:42.730 --> 00:17:43.310 Okay 00:17:50.750 --> 00:17:54.350 Okay, and those are the two solutions 00:17:55.310 --> 00:17:56.990 It's negative 4 00:17:56.990 --> 00:17:58.890 plus the square root of twenty-one, 00:17:59.790 --> 00:18:02.690 and negative four minus the square root of twenty-one. 00:18:03.330 --> 00:18:06.210 Both solutions are irrational numbers 00:18:10.170 --> 00:18:11.770 But that's it 00:18:12.850 --> 00:18:15.450 So we were able to solve this 00:18:16.710 --> 00:18:19.250 Even though it could not be solved by factoring 00:18:22.430 --> 00:18:24.730 Okay, and let me show you something 00:18:30.690 --> 00:18:31.870 This 00:18:31.870 --> 00:18:34.170 Actually does factor 00:18:36.810 --> 00:18:40.770 This would be x and x, right? It's simply 00:18:45.650 --> 00:18:46.330 For 00:18:48.050 --> 00:18:53.504 four plus the square root of twenty-one, and four minus the square root of twenty- 00:18:53.504 --> 00:18:53.770 one. 00:18:54.730 --> 00:18:55.790 So it's fine 00:18:59.610 --> 00:19:03.050 Okay, and there's no way we were gonna guess that right 00:19:03.650 --> 00:19:06.270 The only we guess is integer values 00:19:07.250 --> 00:19:11.350 Okay, and these these two numbers have the same property 00:19:12.090 --> 00:19:15.730 they multiply to be negative 5 and 00:19:17.590 --> 00:19:18.950 They add to be 8 00:19:20.470 --> 00:19:25.090 Okay, they're just not nice whole numbers or integers I should say 00:19:27.250 --> 00:19:32.968 These add to eight: four plus the square root of twenty-one plus four minus the 00:19:32.968 --> 00:19:34.850 square root of twenty-one. 00:19:34.850 --> 00:19:36.730 That's 0 we get 8 00:19:37.590 --> 00:19:39.810 And do they multiply to be negative 5? 00:19:41.730 --> 00:19:44.070 They do let's try it 00:19:53.750 --> 00:19:54.630 16 00:19:56.490 --> 00:20:00.740 Minus four times the square root of twenty-one, plus four times the square root of 00:20:00.740 --> 00:20:01.310 twenty-one, 00:20:04.310 --> 00:20:05.190 Minus 00:20:05.830 --> 00:20:06.330 21 00:20:07.430 --> 00:20:11.010 These terms cancel, and sixteen minus twenty-one gives negative five. 00:20:11.790 --> 00:20:14.970 It's kind of cool. That's pretty cool. It is pretty cool 00:20:20.750 --> 00:20:24.410 Okay, let's try that one and then we'll get to the more difficult 00:20:24.670 --> 00:20:27.110 Again there's no way that's 00:20:27.710 --> 00:20:32.070 Solve this by factoring. So we're gonna complete the square first step 00:20:36.010 --> 00:20:45.450 We gotta get the constant over here and then we complete the square 00:20:52.790 --> 00:20:57.170 We take this number divide by 2 and square 00:21:07.850 --> 00:21:09.910 We add twenty-five to both sides. 00:21:19.590 --> 00:21:21.450 And this definitely factors to 00:21:23.430 --> 00:21:26.890 Half of that number would be over 2 so that's plus 5 plus 5 00:21:37.210 --> 00:21:41.390 And now what square root principle 00:21:45.890 --> 00:21:50.990 X plus five equals plus or minus the square root of twenty-eight. 00:22:11.270 --> 00:22:14.470 Does the square root of twenty-eight simplify? I should have done that first. 00:22:21.890 --> 00:22:22.490 Oh 00:22:22.490 --> 00:22:28.490 There we go, we got our two solutions 00:22:33.870 --> 00:22:38.670 We can now solve quadratic equations when they cannot be factored over the integers, 00:22:38.670 --> 00:22:40.230 or at least are not obviously factorable. 00:22:44.830 --> 00:22:46.450 Let's try that one 00:22:46.450 --> 00:22:49.930 Okay, what's the first thing we do? 00:22:54.070 --> 00:22:55.810 We got to get the constant on the right 00:23:04.150 --> 00:23:06.130 Okay, and we have a little problem on this one 00:23:10.050 --> 00:23:12.710 We want to get x plus or minus some number 00:23:18.750 --> 00:23:20.650 We want just an x here 00:23:22.670 --> 00:23:26.070 We could use square root of two times square root of two, 00:23:27.870 --> 00:23:30.890 Because then that does multiply to be 2x squared 00:23:31.810 --> 00:23:33.430 But it's way too complicated 00:23:35.070 --> 00:23:36.430 Okay, so 00:23:37.150 --> 00:23:39.850 Whenever the leading coefficients not one 00:23:39.850 --> 00:23:44.785 We have to divide both sides by the leading coefficient. We need to change the 00:23:44.785 --> 00:23:46.430 leading coefficient to one 00:23:47.310 --> 00:23:49.890 So we divide by 2 divided by 2 00:23:50.930 --> 00:23:54.770 We get x squared minus 3 over 2x 00:23:55.510 --> 00:23:57.070 5 over 2 00:24:10.750 --> 00:24:13.870 And now we complete the square 00:24:17.510 --> 00:24:23.290 And now we're gonna deal with some fractions and that's okay, this is my B value 00:24:24.670 --> 00:24:28.530 Negative three over two. Take b over two, squared. 00:24:32.870 --> 00:24:37.970 Which is negative 3 over 4 squared which is 00:24:44.650 --> 00:24:46.170 9 16th 00:24:46.170 --> 00:24:47.830 So we add 9 16th 00:25:01.730 --> 00:25:05.090 It's that factors to x plus or minus 00:25:06.030 --> 00:25:08.130 Minus minus what? 00:25:09.650 --> 00:25:16.111 3 over 4 it's the number of before we square it or it's also the square of that but 00:25:16.111 --> 00:25:18.290 then you got to take care of 00:25:18.290 --> 00:25:18.850 the sign 00:25:25.910 --> 00:25:29.370 Okay, and then we got to get a common denominator over here 00:25:35.190 --> 00:25:39.890 That's 40 plus 9 49 over 16 00:25:41.670 --> 00:25:45.570 That right, yes 00:25:52.570 --> 00:25:53.690 Now what 00:25:53.690 --> 00:26:01.553 Something squared equals a number. Use the square root principle: x minus three 00:26:01.553 --> 00:26:02.250 fourths 00:26:03.520 --> 00:26:08.700 equals plus or minus the square root of 49 16th 00:26:16.680 --> 00:26:20.260 Was that 7 over 4? 00:26:50.340 --> 00:26:58.400 Which is 10 fourths or negative 4 fourths? 00:27:04.300 --> 00:27:06.500 which is five halves. Yes. 00:27:20.000 --> 00:27:24.543 This happened to be a perfect square, so we ended up with no square roots. When that 00:27:24.543 --> 00:27:26.220 number is not a perfect square, 00:27:27.340 --> 00:27:30.180 You're gonna end up with square roots in your solution 00:27:37.580 --> 00:27:42.320 We're gonna do it 00:27:42.320 --> 00:27:43.460 You try one more 00:27:43.460 --> 00:27:53.820 Actually, what's the first step? Okay, that's good 00:27:57.940 --> 00:28:03.580 Yeah, man, what's the next step? Okay, you guys are paying attention I like this 00:28:13.740 --> 00:28:15.880 Divide what by two 00:28:17.760 --> 00:28:20.060 Yeah, we sometimes call that the B value 00:28:39.500 --> 00:28:44.720 right, we got to add it to complete the square 00:28:57.680 --> 00:28:59.080 Oh 00:28:59.080 --> 00:29:13.460 Six goes into 144 24. Yes 00:29:13.460 --> 00:29:20.780 What's five times 24 120 plus 49 is 00:29:27.460 --> 00:29:27.820 One hundred sixty-nine. 00:29:38.020 --> 00:29:42.780 Common say we can't do that because uh, this is 13 00:29:43.620 --> 00:29:48.340 Times 13 and this is 12 times 12, but those don't simplify 00:29:50.440 --> 00:29:53.840 But you might be saying something different 00:29:55.140 --> 00:29:58.860 We use the square root principle. 00:29:58.860 --> 00:30:03.083 X minus seven twelfths equals plus or minus the square root of one hundred sixty- 00:30:03.083 --> 00:30:06.420 nine over one hundred forty-four. You were ahead of me, I think. 00:30:10.060 --> 00:30:16.620 Okay, clear it now what 00:30:32.200 --> 00:30:33.600 I 00:30:33.600 --> 00:30:35.300 Like that 00:30:39.800 --> 00:30:43.660 Negative six twelves 00:30:49.500 --> 00:30:52.700 Twenty twelfths which is 00:30:56.100 --> 00:30:56.960 Five thirds 00:31:17.340 --> 00:31:18.180 Oops 00:31:18.180 --> 00:31:21.460 Not an ordered pair: the solution set. 00:31:29.520 --> 00:31:35.980 That was luck it does tell us whenever you get fractions here well 00:31:40.500 --> 00:31:42.520 What was the original equation 00:31:46.640 --> 00:31:47.380 Okay 00:32:05.840 --> 00:32:06.720 This 00:32:06.720 --> 00:32:09.180 This does not factor to this why not 00:32:10.060 --> 00:32:10.660 Because 00:32:12.740 --> 00:32:13.340 Because 00:32:15.100 --> 00:32:19.380 The leading term would not be six x squared, correct? 00:32:20.540 --> 00:32:23.900 However, it's right to X times X is not six X square 00:32:24.540 --> 00:32:30.080 However, all you got to do is stick a six out here now. It does factor into that 00:32:30.080 --> 00:32:36.240 And if you change this to two times three 00:32:39.760 --> 00:32:40.600 Like 00:32:46.240 --> 00:32:48.340 You distributed the 00:32:49.580 --> 00:32:55.880 Two to this guy you get two X plus one and 00:32:57.320 --> 00:32:59.080 Three into this factor gives three 00:33:00.800 --> 00:33:01.640 X 00:33:01.640 --> 00:33:07.700 So we actually could solve this by factoring Wow 00:33:09.440 --> 00:33:09.940 But 00:33:11.560 --> 00:33:12.800 That's kind of crazy 00:33:13.800 --> 00:33:19.572 Okay, all right two numbers that multiply to be negative 30 add to be negative 7 or 00:33:19.572 --> 00:33:19.920 what? 00:33:32.160 --> 00:33:35.260 So we could have solved this by factoring 00:33:35.260 --> 00:33:37.300 changes to 6x squared 00:33:37.900 --> 00:33:44.280 Minus 10x plus 3x minus 5 and a factor by grouping you would have ended up with this 00:33:44.800 --> 00:33:46.660 Wow, okay 00:33:47.940 --> 00:33:52.560 But we didn't need to solve by completing square any 00:33:54.540 --> 00:33:57.920 Any quadratic equation can be solved by completing the square. 00:34:00.400 --> 00:34:04.460 Once in a while and give you an example 00:34:15.100 --> 00:34:15.460 Let's 00:34:15.460 --> 00:34:16.680 Try this one real quick 00:34:19.020 --> 00:34:21.100 We'll be the first step 00:34:23.800 --> 00:34:28.580 Subtract five on both sides. That's right. 00:34:29.410 --> 00:34:34.650 That's right: b over two, squared. Two over two, 00:34:34.650 --> 00:34:34.690 squared 00:34:35.810 --> 00:34:38.490 1 squared 1 so we add 1 to both sides 00:34:51.570 --> 00:34:52.990 Then what do we use 00:34:56.710 --> 00:35:03.930 Square root principle: x plus one equals plus or minus the square root of negative 00:35:03.930 --> 00:35:04.370 four. 00:35:07.170 --> 00:35:10.290 And what is the square root of negative 4 00:35:13.470 --> 00:35:16.870 It's not a real number, okay 00:35:19.290 --> 00:35:20.370 Not real 00:35:21.450 --> 00:35:28.490 There are no real numbers whose square is negative four. 00:35:29.610 --> 00:35:31.770 So what does that tell us about the original? 00:35:32.730 --> 00:35:33.070 equation 00:35:34.510 --> 00:35:35.690 There are no real solutions. 00:35:36.490 --> 00:35:39.490 We often say real because we're gonna learn something else later 00:35:42.350 --> 00:35:45.730 Does it have a solution set yes, yes it is 00:35:47.350 --> 00:35:48.450 The empty set 00:35:50.370 --> 00:35:50.650 Okay 00:35:51.770 --> 00:35:57.748 So if once you use the square root principle and the right hand side is a negative 00:35:57.748 --> 00:35:58.550 you're done 00:35:59.390 --> 00:36:00.650 No real solutions 00:36:01.410 --> 00:36:04.630 Right and to think about it. There's nothing that you could square 00:36:05.250 --> 00:36:08.330 A real square is nonnegative, so it cannot equal this negative number.