Question

Do I need to complete the square if `f(x) = x^2 - 6x + 9`?

Answer 1

You have several options when solving quadratic equations. With this particular problem you could ...

1. Graph it
2. Use Quadratic Formula
3. Factor

Completing the square is not needed here because the equation is already a perfect square trinomial. If you were to complete the square at the end of the process you would have the same exact equation.

`x^2-6x+9=0`

`x^2-6x=-9`

`(-6/2)^2=(-3)^2=9`

Add 9 to both sides

`x^2-6x+9=-9+9`

`x^2-6x+9=0`, same equation

`(x-3)^2=0`

`sqrt((x-3)^2)=sqrt(0)`

`(x-3)=0`

`x=3`

I would have just used the factoring method.

I need the factors of `9` that add up to `-6`. Those factors are `-3` and `-3`.

`0=(x-3)(x-3)`

`x-3=0`
`x=3`