Question

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

Answer 1

Given `y=x^2-8x+7`

Note that if `x^2-8x` are the first two term of a squared expression `(x+a)^2`
then `a= 8/2 = 4` and `a^2 = 16`

`y= x^2 -8x+7`

`= x^2-8x + color(red)(4^2) + 7 color(red)(-16)`

`=(x-4)^2 -9`

Now, the real problem
What do you mean by solve and equation of the form `y =` and expression in terms of `x`?

I will assume you wish to determine the value(s) of `x` for which `y=0` (although this is not obvious).

If `(x-4)^2-9 = 0 (=y)`
then
`(x-4)^2 = 9`

`x-4 = +-sqrt(9) = +-3`

and
`x= 7` or `x=1`