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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.$$x^{2}-12 x=-48$$

$$6 \pm 2 \sqrt{3} i$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Missouri State University

McMaster 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 X squared minus 12 x is equal to negative 48. You'll notice I put a giant blank in there. Yeah, it's out of habit. It's also, I think, a good strategy for you to the floor because the process of completing the square you always take that be value negative. 12 divided by two and then square that number, um, so negative 12. Divided by two is negative. Six. Once I square is 36 and that's the thing is, if you put it in that space, you know, to add 36 to 1 side, and it reminds you that you have to add the same value to the other side as well. And why do we go through that process is now It's easier to find a factor of 36 that adds to be negative. 12. Well, here's your shortcut. It's always this number. Negative. Six. Negative six. But instead operating X minus six twice. We can just write at once Square. That's why I would go through this process. Negative. 48 plus 12 Sorry, 1948 plus 36 is negative. 12. Before moving on, I want to point out that any time we square a number, we better get a positive or zero. So this is impossible for X to be a real solution. Yeah, I'm sure you've gotten practice already with with When you square root you can write down. First of all, the square root mean square will cancel so you have X minus six. On this side. On the right side you have plus or minus. You can have an eye in front. But before jumping any further, you might want to think about rewriting 12 as a square to four times the square to three. Because we know the square to four is, too. I route three. Uh, now there's one more thing to do, and that's the sulfur X. We've got to get rid of this negative six. We can do that by adding six to the right side. Uh, because that's the real part. We always write the real part in front of the imaginary. That's what makes it a complex number. Um, but impossible to write. Three decimals because it's not irrational is complex. That's it's It's customized to Iraq. Three

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