# How do you solve 13p^2-3=4209?

Mar 11, 2017

See the entire solution process below:

#### Explanation:

First, add $\textcolor{red}{3}$ to each side of the equation to isolate the $p$ term while keeping the equation balanced:

$13 {p}^{2} - 3 + \textcolor{red}{3} = 4209 + \textcolor{red}{3}$

$13 {p}^{2} - 0 = 4212$

$13 {p}^{2} = 4212$

Now, divide each side of the equation by $\textcolor{red}{13}$ to isolate ${p}^{2}$ while keeping the equation balanced:

$\frac{13 {p}^{2}}{\textcolor{red}{13}} = \frac{4212}{\textcolor{red}{13}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{13}}} {p}^{2}}{\cancel{\textcolor{red}{13}}} = 324$

${p}^{2} = 324$

Now, take the square root of each side of the equation to solve for $p$. Remember, the square root of a number produces a negative and positive result:

$\sqrt{{p}^{2}} = \pm \sqrt{324}$

$p = \pm 18$