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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.$$x^{2}-3 x-1=0$$

$$\frac{3 \pm \sqrt[2]{13}}{3},-0.303,3.303$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Missouri State University

Campbell 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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I'm gonna solve this. Quadratic X squared, minus three x uh, minus one equals zero. Now, the way I like to do complete the square is put a little space in here and the space over here while I'm at I'm also going to add one to the other side just to cancel that out. Zero plus one is one. So then the next step is always the same. I look at the B value, which is negative three. And I divide that number by two. And in order to complete the square, we're going to square that. Mm. Yeah. So what does that mean? Is that we're multiplying Negative three house by itself and a negative three times negative. Three is positive. Nine and two times two is four. Why can't just add 94 central problem. We also need to add nine force to the other side. And the reason why I would do that is that when you look at the left side, this is a perfect square. Try no mule. And the shortcut is, uh it's always negative. Three house, plus negative. Three houses, negative. Three and negative. Three times negative. Three houses positive. Nine Force That's why this always works. Now, instead of writing X minus three halves twice, we can write it once squared and on the right side we can add this together now. I would rewrite one as four force, so I get the same denominator and four plus four is 13 force, because the denominators the same. So now we're ready to solve this because we can square root both sides. Sam Square urging Topping band. And that's how you square with fractions. So on the left side I still have X minus three halves, and on the right side, I can't really do anything with that. 13. Don't forget about the plus or minus either. Just leave that alone, but I do know the square to four is two. We don't need more than one plus or minus. We can just leave it like that. There's only one thing left to do, and that's add three halves to the right side and you'll notice that the denominators argue the same so I can just combine them together and just leave us three plus or minus Route 13 all over to. And that's your perfect answer. Uh, now, if you actually simplify that. You do get to decimal answers if you want to round. Um mm. But you just need a calculator to do that. And it rounds to 0.303 and the +13 plus is 3.303 So three minus Route 13/2 is the negative answer and three, plus route 13 13 all over two is the positive answer. Sure.

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