# How do you solve x^2 + 4x - 12 = 0 by completing the square?

May 20, 2016

The solutions are color(green)(x = 2 , color(green)(x = -6

#### Explanation:

${x}^{2} + 4 x - 12 = 0$

${x}^{2} + 4 x = 12$

To write the Left Hand Side as a Perfect Square, we add 4 to both sides:

${x}^{2} + 4 x + 4 = 12 + 4$

${x}^{2} + 2 \cdot x \cdot 2 + {2}^{2} = 16$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get
${\left(x + 2\right)}^{2} = 16$

$x + 2 = \sqrt{16}$ or $x + 2 = - \sqrt{16}$

$x + 2 = 4$ or $x + 2 = - 4$

$x = 4 - 2$ or $x = - 4 - 2$

color(green)(x = 2 , color(green)(x = -6