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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.$$12 x^{2}-7 x=12$$

$$-3 / 4,4 / 3$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

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Idaho State University

Lectures

01:17

In each of the following, …

02:52

Solve each of the quadrati…

02:27

02:04

00:49

Solve each equation using …

02:14

02:49

02:11

04:01

02:44

02:41

02:19

02:06

02:50

02:01

02:38

02:13

Alright, We're looking at this quadratic we need to solve by completing the square. And when you complete the square, you need that leading coefficient to equal wine. Uh, so I'm gonna kind of cheat this and just divide everything by 12. That way. 12 2 by by 12. Cancel and I'm left with X squared and just leave at 7. 12 X. Uh, it's okay to to write it this way equals one, um, and putting a blank there. So now we can complete the square by doing half of this be value. Uh, now, I could divide by two. Or in this case, I'm multiplying by 2.5 squared. So looking at negative 7/24 squared, uh, and seven squared is 49 but 576 is to 24 squared. So I also need to add 49/5. 76 to this side. So why did we do that? Is now this left is a perfect square china meal. And so I would go through this process. It's always this number. That's why this process is so nice. And if I get the same denominator on both sides and moving at 5 76 over 5 76 is equal to one. So now I can add those together, Uh, 5, 76 plus 49 for the numerator 6 25. And the denominator stays the same. So now I can solve the square part of this problem. I square rooting both pieces, and that's always square root of fraction. This top and bottoms are looking at X minus 7/24 On the left side, these are both perfect squares. Square to 6. 25 25 square to 5. 76 is 24. Um, So what's really nice about this problem is, in my opinion, I guess is when you're solving for extend, the denominators are already the same. Um, and you just add the seven over seven plus or minus 25 all over 24. So seven minus 25 is negative. 18/24 would reduce to negative three force, and then seven plus 25 all over 24 reduces to four thirds. So those are your perfect answers in this problem

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