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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.$$x^{2}+6 x+3=0$$

$$-3 \pm \sqrt{6},-0.551,-5.449$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Missouri State University

Oregon State University

Idaho State University

Lectures

02:09

Solve each of the quadrati…

02:19

02:49

02:11

03:00

02:04

02:12

02:41

02:44

03:06

03:15

01:01

In each of the following, …

01:03

02:38

04:21

01:07

02:20

02:42

02:14

02:25

our task is the sole this quadratic by completing the square, and, uh, the way I do, this might be slightly different than how your professor does it. But what I'll do is I start by getting rid of this three. I just moved that constant to the other side. Uh, and zero minus three is negative. Three. But then what I'll do is I'll just put a blank right here and a blank over here. The reason why I do that is now I can complete the square. I can look at the six, and this is always the process. Were divided by two squared Well, six divided by two is three squared equals nine. So what I'm gonna do is I'm going to add nine to the left side, and you can't just add nine to one side of an equation. Um, if you add nine to the left, you also have to add nine to the right and the reason why I do that is now the left side is a perfect square China meal. Well, factors of nine that had to be six R three and three. That's why we went through that process. But instead of writing X plus three X plus three twice we write at once squared. This is equivalent to what's up here. If you don't believe me, foil it out on the right side, you have negative three plus nine, which is six. So now we can solve this by square, rooting both sides because the square root we can stop the square. And so on the left side you have X Plus three is equal to Don't forget about plus or minus, because when you square something a negative square, it could give you a positive. And now there's just one more step to do to sulphur. Excuse. Subtract three to the right side. Um, and this is a good answer. Uh, the only thing is that you have to irrational answers. We can have negative three plus Route six, and we can also have negative three minus Route six. So when you use a calculator, you'll see negative three. Plus. Route six is negative zero point 551 whereas name through minus, Route six is negative 5.449 So those are your irrational answers for X X equals there

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