Question

How do you solve `x^2+x-6=0` by completing the square?

Answer 1

`x=2` or `-3`

Explanation:

Moving the `-6` to the right side:
`x^2+x=6`

Completing the square by adding `(b/2)^2` to both sides, where `b` is the second coefficient (in this case, `b=1`):
`x^2+x+(1/2)^2=6+(1/2)^2`
`x^2+x+1/4=6+1/4`
`(x+1/2)^2=25/4`

Simplifying:
`x+1/2=\pm5/2`
`x=-1/2\pm5/2`
`x=4/2` or `-6/2`
`x=2` or `-3`