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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.$$x^{2}-2 x-10=0$$

$$1 \pm \sqrt{11},-2.317,4.317$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Missouri State University

Campbell University

McMaster University

Harvey Mudd College

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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All right, so we're looking at this. Quadratic X squared, minus two X minus 10 is equal to zero. And because we're asked to complete the square, what I typically do is, I believe, a blank right here. So what that means is I need to add 10 to the right side and zero plus 10. This 10. Let me have a blank over here as well. So then your process on completing the square is taking this value that be value negative two divided by two. We always divide by two, and we square that number. Um, so we're looking at negative one squared, which is just positive one. So what I'm doing is I'm adding one to the left side of the equation. If you add one to the left side, you also have to add one to the right side. So why do we do that? Well, now that we do that on the left side now we have a perfect square. Try no meal. That factors of one that had to be negative to our negative one and negative one. That's why we did this process. That's why it's called completing the square. So instead of writing X minus one X minus one Twice we write X minus one. Once squared and on the right side, we know that 10 plus one is 11. So now we can solve the square problem by square, rooting both sides. So on the left side, you just have an X minus. Woman is equal to don't forget. It's plus or minus because you can have a negative number. Once you square, we'll give you positive 11. And then your last step is just to add one to the right side. So one plus or minus the square root of 11. Um, now, the only thing is, the book also wants you to write an irrational answer. So one plus Route 11 as well as one minus Route 11. So if you did that part, uh, you would see that one irrational answer before 0.317 I'm just using it calculated, by the way, at one minus, Route 11 is negative, two 0.317 And those are your two, uh, irrational values for X as well. Um, I would leave. My answer like this, though, is what I prefer

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