How do you solve x2+18x=10 by completing the square?

2 Answers
Chuchubunny · Jacobi J.
Jun 7, 2018

x=−9±√91

Explanation:

For completing the square, you take half the coefficient of the x value, square it, and add it. So in this case, 81 I suppose?
I apologize, I don't quite remember how to do this. However there is already a 10...

Oh! I got it!

So add 91 and then you would get:

x2+18x+81=91

Then you factor:

(x+9)2=91

Square root:

x+9=±√91

Solve by subtracting 9:

x=−9±√91

And that should be your answer.

Bill Jorgensen
Jun 7, 2018

x=−9±√91

Explanation:

ax2+bx+c

To complete the square a must be 1 (which it is) and:

c=(b2)2

x2+18x=10

x2+18x+c=10+c

notice we have to add c to both sides of the equation so we don't alter the value.

c=(182)2=81

x2+18x+81=10+81

now factor the left side:

(x+9)(x+9)=91

(x+9)2=91

now we solve:

√(x+9)2=±√91

x+9=±√91

x=−9±√91

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