# How do you solve p^2 - 3p =8 by completing the square?

Jul 20, 2017

See below.

#### Explanation:

We want to complete the square for the left side. We can find the constant value as we know the coefficient of the $p$ term, which is $- 3$. We divide this by $2$, and then square the resulting value.

The constant term is just : ${\left(- \frac{3}{2}\right)}^{2} = \frac{9}{4}$.

${p}^{2} - 3 p + \frac{9}{4} = 8 + \frac{9}{4}$
${\left(p - \frac{3}{2}\right)}^{2} = \frac{41}{4}$
$p - \frac{3}{2} = \pm \frac{\sqrt{41}}{2}$
$p = \pm \frac{\sqrt{41}}{2} + \frac{3}{2}$.