Question

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

Answer 1

`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.

Answer 2

`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)`