# How do you solve the quadratic equation by completing the square: p^2 + 12p = 13?

Jul 15, 2015

I found:
${p}_{1} = 1$
${p}_{2} = - 13$

#### Explanation:

You can try by adding and subtracting $36$ on the left to get:
${p}^{2} + 12 p \textcolor{red}{+ 36 - 36} = 13$
and rearranging:
${p}^{2} + 12 p + 36 = 13 + 36$
${\left(p + 6\right)}^{2} = 49$
square root both sides:
$p + 6 = \pm \sqrt{49} = \pm 7$
so you get:
${p}_{1} = - 6 + 7 = 1$
${p}_{2} = - 6 - 7 = - 13$