Question

When solving `x^2 – 4x = –7` by completing the square what value is added to both sides of the equation?

Answer 1

Your question is equivalent to asking:
What value needs to be added to `x^2-4x`
to make the expression a square of the form
`(x+a)^2 = x^2+2ax +a^2`

We have `2ax = -4x`
`rarr a=-2`

So `a^2 = 4`

We need to add `4` to `x^2-4x` in order to complete the square.