Question

How do you factor and solve `m^2=-6m-7`?

Answer 1

`m =sqrt2-3" or " m=-sqrt2-3`

Explanation:

`m^2 =-6m-7`

`m²+6m+9=-7+9" add "(6/2)^2` to both sides
`(m+3)²=2`

`(m+3)^2 - 2=0" "` factor as difference of squares

`(m+3+sqrt2) (m+3-sqrt2)=0`

`m+3=sqrt2 " or " m+3=-sqrt2`

`m = sqrt2-3" or "m= -sqrt2 -3`