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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.$$(x-3)(x+5)=12$$

$$-1 \pm 2 \sqrt{7},-6.29,4.29$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

McMaster University

Baylor University

University of Michigan - Ann Arbor

Lectures

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Solve each of the quadrati…

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In each of the following, …

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we're looking at this quadratic, which is X minus three X plus five, is equal to 12. So the first thing you want to do is distribute, so distribute X in there, So x squared plus five x distribute that negative three in there, some negative three x negative. Three times five is negative. 15 is equal to 12. Leave that 12 alone. So what you'll see next is that I mean, combine like terms. Five x minus three X s two x and I like to leave a blank right there. Also put a blank over here because I'm also going to add 15 to the right side. 12 plus 15 is 27 and now I can complete the square because I can follow my process that we've established two divided by two. You always take this number divided by two and then square it well to divide by two is one when I square that I get one. So I'm going to add one to the left side. Well, if I add one to the left side, I also have to add one to the right side. That's why I put a blink right there. It's the only way that that works. The reason why we do that is the left side is a perfect square. Try no mule factors have one that had to be two are one and one. Instead of writing one twice we can write up. Once squared, it's always that number. On the right side, we get 28. The reason why we do that is we can square root to solve the square problem. Square root mean square will cancel. And for those who need help, I would rewrite 28 as four times seven because I know the square root of four is, too. Just make sure you're right plus or minus two. Route seven left with X plus one on the left side to solve for X. Just subtract one to the right side, so this is a perfect answer. But if you go to a calculator and go to type in negative one minus two Route seven, you'll get negative 6.290 and made one plus two. Route seven is 4.290 So these are the rounded answers to three estimates or this kind of answer

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