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

Sep 13, 2014

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

1. Graph it
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.

${x}^{2} - 6 x + 9 = 0$

${x}^{2} - 6 x = - 9$

${\left(- \frac{6}{2}\right)}^{2} = {\left(- 3\right)}^{2} = 9$

${x}^{2} - 6 x + 9 = - 9 + 9$

${x}^{2} - 6 x + 9 = 0$, same equation

${\left(x - 3\right)}^{2} = 0$

$\sqrt{{\left(x - 3\right)}^{2}} = \sqrt{0}$

$\left(x - 3\right) = 0$

$x = 3$

I would have just used the factoring method.

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

$0 = \left(x - 3\right) \left(x - 3\right)$

$x - 3 = 0$
$x = 3$