# How do you solve 7p^2+16=2151?

May 30, 2017

$\pm 17.5$

#### Explanation:

First rearrange the equation to have all like terms on one side and unlike terms on the other:

$7 {p}^{2} = 2135$

Divide by $7$ to get $p$ on its own and then square root it.

${p}^{2} = 305$
$\sqrt{{p}^{2}} = \pm \sqrt{305}$

$p = \pm \sqrt{305}$

$= \pm 17.4642492$

$= \pm 17.5$ (to 3 sf)

May 30, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{16}$ from each side of the equation to isolate the $p$ term while keeping the equation balanced:

$7 {p}^{2} + 16 - \textcolor{red}{16} = 2151 - \textcolor{red}{16}$

$7 {p}^{2} + 0 = 2135$

$7 {p}^{2} = 2135$

Next, divide each side of the equation by $\textcolor{red}{7}$ to isolate ${p}^{2}$ while keeping the equation balanced:

$\frac{7 {p}^{2}}{\textcolor{red}{7}} = \frac{2135}{\textcolor{red}{7}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} {p}^{2}}{\cancel{\textcolor{red}{7}}} = 305$

${p}^{2} = 305$

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

$\sqrt{{p}^{2}} = \pm \sqrt{305}$

$p = \pm 17.464$ rounded to the nearest thousandth.