Solve Using the Square Root Property 2n^2=-144

$2 n^{2} = - 144$

Step 1

Divide each term in $2 n^{2} = - 144$ by $2$ and simplify.

Divide each term in $2 n^{2} = - 144$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $n^{2}$ by $1$ .

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

Simplify the right side.

Divide $- 144$ by $2$ .

$n^{2} = - 72$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$n = \pm \sqrt{- 72}$

Step 3

Simplify $\pm \sqrt{- 72}$ .

Rewrite $- 72$ as $- 1 (72)$ .

$n = \pm \sqrt{- 1 (72)}$

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$n = \pm \sqrt{- 1} \cdot \sqrt{72}$

Rewrite $\sqrt{- 1}$ as $i$ .

$n = \pm i \cdot \sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$n = \pm i \cdot \sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

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

Pull terms out from under the radical.

$n = \pm i \cdot (6 \sqrt{2})$

Move $6$ to the left of $i$ .

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

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$n = 6 i \sqrt{2}$

Next, use the negative value of the $\pm$ to find the second solution.

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

The complete solution is the result of both the positive and negative portions of the solution.

$n = 6 i \sqrt{2}, - 6 i \sqrt{2}$