# How do you solve 8n^2-6=306?

Mar 25, 2017

See the solution process below:

#### Explanation:

First, add $\textcolor{red}{6}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$8 {n}^{2} - 6 + \textcolor{red}{6} = 306 + \textcolor{red}{6}$

$8 {n}^{2} - 0 = 312$

$8 {n}^{2} = 312$

Next, divide each side of the equation by $\textcolor{red}{8}$ to isolate ${x}^{2}$ while keeping the equation balanced:

$\frac{8 {n}^{2}}{\textcolor{red}{8}} = \frac{312}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} {n}^{2}}{\cancel{\textcolor{red}{8}}} = 39$

${n}^{2} = 39$

Now, take the square root of each side of the equation to solve for $x$ while keeping the equation balanced. Remember, when taking the square root of a number there is a negative and positive result:

$\sqrt{{n}^{2}} = \pm \sqrt{39}$

$n = \pm \sqrt{39} = \pm 6.245$ rounded to the nearest thousandth.