Question

How does one factor `9x - 8 = x^2` ?

Answer 1

`(x-8)(x-1)=0`

Explanation:

Given `9x-8=x^2`

Re-arranging the terms:
`color(white)("XXX")x^2-9x+8=0`

with factors:
`color(white)("XXX")(x-8)(x-1)=0`

Answer 2

`x^2-9x+8=(x-1)(x-8)`

Explanation:

`9x-8=x^2`

`x^2-9x+8=0`

`x^2-9x+8=(x-1)(x-8)`

Answer 3

`(x-1)(x-8) = 0`

The equation can be solved to give `x = 1, x = 8`

Explanation:

As it is a quadratic trinomial, make it equal to 0, with `+x^2`

`x^2-color(orange)9x color(magenta)(+) color(blue)8 = 0`

Find factors of `color(blue)8` which `color(magenta)(add)` up to `color(orange)9 " 1 x 8"`

The signs are the `color(magenta)(same)`, they will both be negative.

This gives `(x-1)(x-8) = 0`

Once factored, the equation can be solved to give

`x = 1, x = 8`