Question

How do you solve using the completing the square method `x^2+6x=7`?

Answer 1

Create a perfect square trinomial on the left side, and your solution is not far away!

Explanation:

First, the lead coefficient should = 1 to make this easiest.
Then, take half of the linear coefficient, then square it. Add to both sides:
`x^2+6x+9=7+9`
Factor the left:
`(x+3)^2=16`
Take the square root of both sides:
`sqrt((x+3)^2)=sqrt(16)`
Left side inverse operations undo each other, on the right side, don't forget the `+-` on the right!

`x+3=+-4`

so `x + 3 = 4` or `x + 3 = -4`

so x = 1 or -7.