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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.$$x^{2}+10 x+50=0$$

$$5 \pm 5 i$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

02:12

Solve each of the quadrati…

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02:01

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02:25

01:16

In each of the following, …

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02:00

02:23

01:11

02:14

02:41

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04:01

We're looking at X squared plus 10 X Plus 50 and were asked to complete the square. So to do that, what I usually do is just leave the exporting 10 x alone. Put a little blank. What I'm technically doing is subtracting 50 over zero minus 15 is negative. 50. So now I can complete the square, which is taking this number 10. You divided by two and then you square that number. It's always the same process of 10 divided by two is five. Squared is 25 so I get to add 25 to both sides. You might be sitting there saying, Why is a If you add a number to one side of the equation, have to add it to the other? And why do we do that is now The left side is a perfect square. Try no meal factors are 25 that had to be 10 or five and five. But instead of writing X plus five X plus five, we can write X plus five once squared and then on the right side we can simplify that to be negative. 25 negative 15 plus 25 equals that now we're ready to solve because we can square root both sides the square root. We can start the square. We're left with X plus five Anytime you square root and you're solving your answers of plus or minus, the square to 25 is five. In the squared of a negative, you have to put an eye in that problem. Now there's only one thing left to do, and that's to subtract five over negative five plus or minus five. I That's your final answer. There's no way to simplify that, because this is a complex number with a real part in an imaginary part. So there's no way to write the three decimals down, so this is it.

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