Question

How do you solve by completing the square: `x^2 +8x = 7`?

Answer 1

Since `(x+a)^2 = x^2+2ax + a^2`

If `x^2 +8x` are the first 2 terms of a squared expression
the third term must be `(8/2)^2 = 16`

Add `16` to each side of the equation, giving
`x^2+8x+16 = 23`
which is the same as
`(x+4)^2 = 23`

Taking the square root of both sides
`x+4 = +-sqrt(23)`

`x= -4 + sqrt(23)`
or
`x=-4-sqrt(23)`