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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.$$x^{2}-4 x=8$$

$$2 \pm 2 \sqrt{3},-1.464,5.464$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Missouri State University

Harvey Mudd College

Idaho State University

Lectures

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Solve each of the quadrati…

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In each of the following, …

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Use the quadratic formula …

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Solve each quadratic equat…

Okay, so we're looking at X squared minus four. X is equal to eight. So what I like about this problem is it's already set up to complete the square. Um, notice that put some links in here. It helps me visualize. So maybe it helps you as well. And to complete the square, it's always the same process. You take that be value, which is negative for this product place divided by two and then square. That number negative four divided by two is negative. Two. Now I have two squared is positive for So if I add for to the left side I also need to add forward to the right side. If you're sitting there and thinking, Why do you do that? Well, if you look in the left side, this is now a perfect square. China me on that factors of four that had to be negative four are negative to negative two. Some people would write that out X minus two times X minus two. And if you foil that, you'll see that these two things are equivalent. But instead of writing it that way, we can write it as just one term, explains two squared, and on the right side, eight plus four is equal to 12 and see exactly where I got that from. So now we can solve this square problem by square, rooting both sides. Square root in the square will cancel, and just real quick. The square to 12 is equal. Doesn't square to four times a square. 23 If you're curious why I chose four. That's a perfect square. And I know the square root forest, too. Don't forget about plus or minus because you can square negative numbers and then root three stays the same. So there's only one more thing left to do. And that's the add two to the right side. We always put the real or the integer whole number, uh, in front of the radical. Now, if you actually figured out to minus, Route three is negative. 1.464 and two plus two. Route three is 5.464 So these are the irrational answers for X Yeah,

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