Question

How do you solve by completing the square: `x^2 - 8x - 1 = 0`?

Answer 1

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

If we are going to replace
`x^2-8x-1`
with
`x^2-8x+16`
we will need to add `+17` to both sides of the equation

`x^2-8x+16 = 17`

re-write the left-side as a square
`(x-4)^2 = 17`

then take the square root of both sides
`x-4 = +-sqrt(17)`

`rarr x = 4+sqrt(17)` or `x = 4 -sqrt(17)`