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

Apr 16, 2018

n = ± 6isqrt{2}

#### Explanation:

$2 {n}^{2} = - 144$

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

n = ± sqrt{-72}

The square root of a negative number will always involve complex numbers.

n = ± isqrt{72}

Since $\frac{72}{6} ^ 2 = 2$

n = ± 6isqrt{2}

Apr 16, 2018

$n = \pm 6 \sqrt{2} i$

#### Explanation:

$\text{divide both sides by 2}$

$\Rightarrow {n}^{2} = - \frac{144}{2} = - 72$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\Rightarrow n = \pm \sqrt{-} 72 \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\left[\sqrt{-} 72 = \sqrt{36 \times 2 \times - 1} = \sqrt{36} \times \sqrt{2} \times \sqrt{- 1}\right]$

$\Rightarrow n = \pm 6 \sqrt{2} i$