# How do you solve the quadratic equation by completing the square: r^2 + 14r = -13?

Jul 16, 2015

The solutions for the equation are:
color(blue)(r = -1 , r=-13

#### Explanation:

${r}^{2} + 14 r = - 13$

To write the Left Hand Side as a Perfect Square, we add 49 to both sides
${r}^{2} + 14 r + 49 = - 13 + 49$

${r}^{2} + 14 r + 49 = 36$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get
${\left(r + 7\right)}^{2} = 36$

$r + 7 = \sqrt{36}$ or $r + 7 = - \sqrt{36}$

$r + 7 = 6$ or $r + 7 = - 6$

color(blue)(r = -1 or r=-13