How do you solve 2n^2=-144?

Feb 16, 2017

See the entire solution process below:

Explanation:

First, divide each side of the equation by $\textcolor{red}{2}$ to isolate the ${n}^{2}$ term while keeping the equation balanced:

$\frac{2 {n}^{2}}{\textcolor{red}{2}} = - \frac{144}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} {n}^{2}}{\cancel{\textcolor{red}{2}}} = - 72$

${n}^{2} = - 72$

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

$\sqrt{{n}^{2}} = \sqrt{- 72}$

There is no real solution to this problem. You cannot take the square root of a negative number.