# How do you solve the quadratic equation by completing the square: x^2+8x-2=0?

Jul 19, 2015

color(green)(x = sqrt 18 - 4 or  color(green)(x = -sqrt 18 -4

#### Explanation:

${x}^{2} + 8 x = 2$

To write the Left Hand Side as a Perfect Square, we add 16 to both sides.

${x}^{2} + 8 x + 16 = 2 + 16$

${x}^{2} + 2 \cdot 4 \cdot x + {4}^{2} = 18$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get
${\left(x + 4\right)}^{2} = 18$
$x + 4 = \sqrt{18}$ or $x + 4 = - \sqrt{18}$
color(green)(x = sqrt 18 - 4 or  color(green)(x = -sqrt 18 -4