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

$$4 \pm 2 \sqrt{5},-0.472,8.472$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:13

Solve each of the quadrati…

02:50

02:23

02:20

01:13

In each of the following, …

01:11

02:52

01:29

02:27

01:07

01:23

02:04

Use the quadratic formula …

02:38

02:12

Solve each quadratic equat…

02:19

02:06

01:12

we're giving this quadratic of X squared minus eight X is equal to four, and you probably noticed I left a giant space in here. It's just a habit of mine because I think it's helpful for students to recognize that completing the square you take that be value divided by two, and then you square it well. Negative eight, Divided by 42 is negative for when you square, you get 16. So that's the number that you need to add to the left side. Now, to keep things equal, you also have to add 16 to the right side. And the reason why we do that is now the left side is a perfect square. Trying Amiel and Factors is 16. That had to be negative. Eight are negative. Four negative four plus negative for is negative 84 times negative for is positive 16. So instead of writing X minus four, twice expense for expense for we can write it X minus four squared and on the right side we can equal 20. The reason why we do that is now we can solve the square part of this problem by square rooting square root and, uh, the square root of 20 we could actually rewrite as the square to four times a spurt of five. I think that's helpful for some students to recognize that we have X minus four is equal to well, don't forget about plus or minus. When you square root, you can get a negative answer. The square root of four is two square to five. We don't know, so we'll leave it like that. And I hope I don't know if I explained it, but four times five is 20. That's where I got those numbers from. And there's one more step is to get rid of this negative four. We'll add it to the right side. We always put that whole number in front of the irrational to five. This is a perfect answer now for clarity. Um, some people might want to recognize that there are two answers here. There's four plus two Route five and then also for minus two. Route five and I would need a calculator to figure out those values, but they are correct. Irrational numbers 8.472 if you use a calculator and four minus two or five as negative 0.472 So these are correct. So I got a certain yeah,

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