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Solve each of the quadratics by first completing the square. When the roots are irrational, also give the solutions to the nearest one thousandth.$$(2 x-3)(3 x+1)=-4$$

$$1,1 / 6$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

02:41

Solve each of the quadrati…

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02:12

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In each of the following, …

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02:49

01:10

Solve each equation by fin…

02:04

All right. So we have this Quadratic might not look like quadratic quite yet, but it is, and I'll show you. It is when I foiled this out. So as I distribute, I get six xq swears Excuse me. Two x times one is two x banana distribute this negative three in there. So that's minus nine X 93 times one is negative. Three is equal to negative four still. So as I combine my terms, what I would do is, uh, just leave that six x squared alone for now, two X minus nine X is negative. Seven X. I like to put a blank right here, but I actually do one more thing here. Surely I'm also going to add three to the right side. This is how I like to complete the square. Like I said, I'll put a blank right here. Now, when you complete a square, you want this leading coefficient to be, uh, one. So what I usually do is factor out a six. Now, you don't have to do that to both sides because I'm only factoring out of six on this left side. So I'm going to leave this negative one of them. But you'll see how that impacts my answer over here. Because as I do, the process of completing square I mean, I do half of this number. Um, and typically, I write divided by two. But notice I said time half of it divided by two and multiply by one half of the same thing and then squared. So we're looking at Mega 7 12 to multiply fractions straight across. So that's 49 over 144 now. Technically, I'm not adding 49 over 144. What I'm adding is distributing the six in there. Um and uh huh. Six goes into 144 24 times. So, technically, what I'm adding as I distribute that in there is, uh, let's see, because six goes into 144 24 times, you're really adding 49/24. So that's what I'm going to add over here. Uh, and if you were to distribute to, that's the value that's being added to the left side. So the reason why I do that is now I can do this perfect square trim O nial And it breaks down to this number 7/12 being squared. Now, as I look at the right side, what I would do is actually change one to be negative. 24/24. That way I can add and get the denominators to be the same. And 49 minus 24 is 25. And before you solve a square problem, you have to get rid of this number in front. So I'm going to multiply instead of dividing by six. I'm going to multiply by 16 So which means I need to do 24 times six, which is 144. So what do we have? We have X minus 7. 12 squared is equal to 25 over 144. Why is that useful? Well, now we can square root both sides, and I know the square root of 25 and I know the square root of 144 cluster main minus five 12, the square root of each piece. And this is even helpful because as I add 7 12 to each side, I can get the same denominator. The Niners are really the same. So seven plus five is 12, 12 and seven. Minus five is too 12. Those are my two answers for X, but they both reduce 12. 12 is one. And to trust is 16 Your two answers. Yeah.

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