# How do you solve using the completing the square method x^2+8x+15=0?

Apr 11, 2016

The solutions for the equation are:
color(green)(x = - 3  , color(green)(x = -5

#### Explanation:

${x}^{2} + 8 x + 15 = 0$

${x}^{2} + 8 x = - 15$

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

${x}^{2} + 8 x + 16 = - 15 + 16$

${x}^{2} + 2 \cdot x \cdot 4 + {4}^{2} = 1$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get

${\left(x + 4\right)}^{2} = 1$

$x + 4 = \sqrt{1}$ or $x + 4 = - \sqrt{1}$

$x = \sqrt{1} - 4$ or $x = - \sqrt{1} - 4$

$x = 1 - 4$ or $x = - 1 - 4$

color(green)(x = - 3  or  color(green)(x = -5