# How do I complete the square if f(x) = 3x^2 + 12x - 9?

Sep 13, 2014

Begin by adding 9 to both sides of the equation.

$3 {x}^{2} + 12 x = 9$

Factor out a $3$ from the left side of the equation.

$3 \left({x}^{2} + 4 x\right) = 9$

Locate the $x$ term and take half of the coefficient and square it

${\left(\frac{4}{2}\right)}^{2} = {2}^{2} = 4$

Add $3 \cdot 4$ to the right side of the equation. Because we factored out a $3$.

On the left side add $4$ within the parenthesis.

$3 \left({x}^{2} + 4 x + 4\right) = 9 + 12$, Perfect square trinomial

$3 {\left(x + 2\right)}^{2} = 9 + 12$

$3 {\left(x + 2\right)}^{2} = 21$

${\left(x + 2\right)}^{2} = 7$, Divide by 3

$\sqrt{{\left(x + 2\right)}^{2}} = \sqrt{7}$

$x + 2 = \pm \sqrt{7}$

$x = \pm \sqrt{7} - 2$