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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.$$6 x^{2}+5 x-6=0$$

$$-3 / 2,2 / 3$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

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Lectures

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Solve each of the quadrati…

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In each of the following, …

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Solve each equation using …

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So we're solving this by completing the square. Solving this quadratic and what you need to do in order to complete the square is make sure you're leading coefficient is one. So I'm gonna I'm just gonna divide every piece by six. And this is only okay when I'm solving, uh, if you're trying to graft this quadratic, that's not really okay, because you're changing where the Vertex is located. Um, but in the in the grand scheme of things, this is okay. And, uh, what I'm also going to do is move this term to the other side. So negative 65 by six is negative. Once I'm gonna add one to the right side. Cancel that out. And zero plus one is one. So now what I'm ready to do is complete the square, and I can do that by taking this. Be value, uh, and dividing it by two. Or sometimes they say, multiply by one half because you want half of that value square. So the reason why do multiply by one half is to help students realize that use multiple straight across 5/12. Well, when you square five, you get 25 when you square 12, you get 144. Now you have to add to both sides of the equation. So the reason why we do that is then the left side is a perfect square. Try No me. Um and there's factors. Of 25/1 44 that had to be 56 it's always this number. So we're looking at X plus 5. 12 squared and on the right side, I would just change 1 to 144 over 144. That way we can add the enumerators denomination now the same. Uh, so that's 100 and 69. So it's really nice about this pounds when you solve the square by square rooting, Sad cancels out with this. The X Plus 5 12 is equal to plus or minus. I know the square 169. I know the square root of 140. So now all I have to do is sulfur X by subtracting 5 12 school. Maybe the most complicated thing, though, is to recognize that it's 13 12, minus 5, 12 and negative 13, 12, minus five twice So not the same value. So 13 minus five is eight and negative. 13 minus five is negative. 18 dinar stays the same, but each of those reduced to two different numbers like those are both divisible by four. So you get two thirds. These are both visible by six. So you get negative. Three abs, Are you two answers? There you go.

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