Question

How do you solve `x^2 + 6x + 7 = 0` by completing the square?

Answer 1

Note that `color(red)(x^2+6x+9) = color(blue)((x+3)^2)`

Given `x^2+6x+7=0`
we can rewrite this as
`color(red)(x^2+6x+9) -2 = 0`

`color(blue)((x+3)^2) = 2`

`x+3 = +-sqrt(2)`

`x=-3+-sqrt(2)`