Question

How do you solve using the completing the square method `x^2-8x+7=0`?

Answer 1

`x=7color(white)("XX")orcolor(white)("XX")x=1`

Explanation:

Given
`color(white)("XXX")x^2-8x+7=0color(white)("XX")`Note: I modified the question to include the `color(blue)(=0)`

Then
`color(white)("XXX")x^2-8x=-7`

Remembering the general relation:
`color(white)("XXX")x^2+2ax+a^2 = (x+a)^2`

If `x^2-8x` are to be the first two terms of `x^2+2ax+a^2`
then
`color(white)("XXX")a=-4`
and
`color(white)("XXX")a^2=16`

So we will need to add `16` (to both sides) to `underline("complete the square")`

`color(white)("XXX")x^2-8x+16 = -7+16`

`color(white)("XXX")(x-4)^2=9`

`color(white)("XXX")x-4=+-3`

`color(white)("XXX")x=4+-3`

`color(white)("XXX")x=7color(white)("XX")orcolor(white)("XX")x=1`