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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.$$6 x^{2}+23 x=-20$$

$$-5 / 2,-4 / 3$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Lectures

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Solve each of the quadrati…

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In each of the following, …

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So we're given this quadratic. Yeah, but if we're asked to complete the square what you want to have happened? It was this leading coefficient should equal one. Well, we can do that by dividing everything in the problem by that number. Now, I'm gonna leave these as fractions, which I know. Some people do not like fractions, but it actually makes sense. And you could reduce this if you want, Like, dividing both of those by two. So you get negative 13th. But the whole premise of completing the square as you take that be value cut in half. Some people divide by two. In this case, I'm multiplying by one half, Um, and then squaring that number. So what I'm doing is I have 23 12th that needs to be squared. And that's the number that we're going to add to both sides. 23 23 squared is 5, 29 and 12 square is 144. So you got to add 5. 29/1. 44 to both sides. So on the left side, this is a perfect square. Try no meal. Uh, and the shortcut is it's always this number. Whatever B divided by two is That's the the thing that multiplies to be five that blue thing and adds to be listening. Uh, so with a lot of practice, it makes perfect sense. If you're learning this for the first time, it might not be so easy. So on the right side, though, we have to add together those values. And as I just typed it into the calculator, I got 49/1 44. You might get the same denominators between the two of them and then Adam together. I don't know, it would be best for you, but now we're ready to solve this because we can undo the square by square, rooting both sides in the square root of fraction Just do top and bottom. So on the left side, you just left with that X plus 23/12. On the right side, you have this plus a minus square to 49. 7 square root of 144 is 12, and the only thing left to do now is to subtract that 23 over. And what's nice is the denominators are the same, so we can just do 23 plus or minus seven all over 12. Because the denominator already the same. So as you're doing that, you might notice a negative 23 minus seven would be negative. 30 over 12 and May of 23 plus seven is negative. 16 over 12. So then your values for X. When you reduce it, they're both visible by six. You would get negative five halves for that one. These are both divisible by four. So you're at negative four thirds. Are you too Rational Solutions?

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