How do you solve x2+18x+80=0 by completing the square?

2 Answers
Gió
Jul 10, 2015

I found:
x1=−8
x2=−10

Explanation:

Start by taking 80 to the right and get:
x2+18x=−80
now you need a number that multiplied by 2 gives 18...could be 9!
So, add and subtract NOT 9 but 92=81!
x2+18x+81−81=−80
take −81 to the right:
x2+18x+81=81−80
so that you can write:
(x+9)2=1
root square both sides:
x+9=±√1=±1
So you get two solutions:
x1=−8
x2=−10

Alan P.
Jul 10, 2015

x=−8
or
x=−10

Explanation:

Given : x2+18x+80=0

Complete the square:
XXXXx2+18x+(182)2−(182)2+80=0
Simplify:
XXXXx2+18x+92−81+80=0
Write as a squared binomial:
XXXX(x+9)2−1=0
Move the constant to the right side
XXXX(x+9)2=1
Take the square root
XXXXx+9=±1
Move constant to the right side
XXXXx=−10 or x=−8

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