# How do I complete the square if f(x) = x^2 + 4x - 9?

Sep 13, 2014

We will begin by moving the constant value to the other side of the equation.

Next we will find a value to add to both sides of the equation. This value will create a perfect square trinomial which will greatly aid us in finding the solution to this problem.

We next find the coefficient of the $x$ term and divide it by 2 and then square it. This result will be added to both sides of the equation. This creates the perfect square trinomial. Because we add this value to both sides of the equation it will remain balanced.

${x}^{2} + 4 x = 9$

${\left(\frac{4}{2}\right)}^{2} = {\left(2\right)}^{2} = 4$, This is the value to be added to both sides

${x}^{2} + 4 x + 4 = 9 + 4$

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

${\left(x + 2\right)}^{2} = 13$

$\sqrt{{\left(x + 2\right)}^{2}} = \sqrt{13}$

$x + 2 = \pm \sqrt{13}$

$x = \pm \sqrt{13} - 2$