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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.$$(x+3)(x+2)=-10$$

$$\frac{-5 \pm \sqrt{39 i}}{2}$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

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Solve each of the quadrati…

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we're giving this quadratic at plus three times X plus two is equal to negative 10. So the first thing to do in this problem is to distribute that X into each piece as well as distributing the three into each piece. And three times two is six. I'm not doing anything with that negative 10, but now what I need to do is combine like terms. So x squared plus five X and I'd like to put a space right here, as well as a space on this side and all I'm going to do next to subtract the six over. So we're looking at negative 16 on this side, and now we're ready to complete the square, which is the process of taking this number divided by two and then squaring that piece. So just a reminder that squaring means multiply by itself and we multiply fractions straight across. That's why we get 25 force. So on this side, I also have 25 force. The reason why we do that is that on this side we have a perfect square, Trine Amiel and the shortcut is it always factors to this number five halves. Well, it's always be divided by two. This case, it is five half squared. Um, And on this side, what I would do is actually change, uh, to get the same denominator. So 16 is the same as negative 64 force. And then when I add 25 to it, I get negative 39. And the denominators are the same sort of force. And we do that because now we can square root both sides and to square two fractions, just square root, top and bottom. So that cancels out the square. They're left with this X plus five halves on the left side, on the right side. Well, first of all, if we haven't square root of a negative, we need an eye. Plus or minus. I don't want to square to 39 its factors are only prime numbers. I'm talking about three and 13. Um, there's no perfect squares there, but the square to for is to, And the last step to do is to get this five halves to the right side. You do that by subtracting, because the denominators are saying we can actually combine them together as a single denominator. Any time you add or subtract. Um, the designers have to be the same, and then you can combine them to single fraction. And that's it. That's your answer. It's a complex route.

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