How do you solve x^2+18x=10 by completing the square?

2 Answers
Jun 7, 2018

x=-9 +-sqrt91

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:

x^2+18x+81=91

Then you factor:

(x+9)^2=91

Square root:

x+9=+- sqrt91

Solve by subtracting 9:

x=-9+-sqrt91

And that should be your answer.

Jun 7, 2018

x= -9+-sqrt(91)

Explanation:

ax^2+bx +c

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

c=(b/2)^2

x^2+18x=10

x^2+18x + c =10+c

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

c=(18/2)^2= 81

x^2+18x + 81 =10+81

now factor the left side:

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

(x+9)^2= 91

now we solve:

sqrt((x+9)^2)= +-sqrt(91)

x+9= +-sqrt(91)

x= -9+-sqrt(91)