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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.$$x^{2}+5 x=5$$

$$\frac{-5 \pm 3 \sqrt{5}}{2},-5.854,0.854$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

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University of Michigan - Ann Arbor

Lectures

02:38

Solve each of the quadrati…

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01:05

In each of the following, …

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02:01

00:59

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03:00

01:33

Solve each equation using …

02:41

Okay, We have the quadratic X squared plus five X is equal to five and notice. I left myself some room here because I'm going to add a number to both sides. What's that number going to be? Well, it's always the same process in completing the square. You look at this medal number, which is five divided by two squared now, I don't know. I mean, I do know, but I'm just reminding you that when you square a fraction, it's just multiplying. Show you across. Five times five is 25 and two times two is four. So on the left side, um, I'm gonna add 25 force, And, uh, if you add 25 force to the left side, you also have to add 25 force to the right side. Now, if we look at the left side closely, that's a perfect square. Try no meal now so we can factor this. And here's a trick for you is a perfect square. Try no meal in the process of doing five divided by two. That's always the number that goes right here squared. If you don't believe me foiled out and see that you get the same answer. Now on the right side, I would actually change five to be 24th. You know, I'm getting the same denominator as what I have over here. Um, again 20 divided by four is five. That's where I got that from. But the reason why I would do that is now I can get the same denominator 45 force, and I can add them together. And now that math is actually pretty easy to do because I can square root both sides and square rooting of fractions to square rooting top and bottom. And I would actually rewrite the top is route nine times, Route 59 times five is 45. And I chose that for a reason because I know the square root of nine. So on the left side of the square root mean square cancel left with this X plus five halves on the right side, I have plus or minus. Don't forget, you can get a negative answer. I know the square to nine is three. I know the square before is to the only thing I don't know is that Route five and we're pretty much done. All we have to do is subtract five halves over and again. It's the same denominator, so I can actually combine them into a single denominator because the denominator is the same and this is a perfect answer. Now, the only thing is they ask you to rewrite. This is, uh, you know, you can do negative five plus three or five all over to the negative. Five minus 3 to 5 all over too. If you use a calculator for that, you get negative. Five 0.8 to 4. Okay? Nope. 854 Make sure you typed that into your calculator correctly or zero 0.854 Just double checking into them. Those are rounded answers for this problem, so mhm.

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