Solve Using the Square Root Property -7n^2=-448

$- 7 n^{2} = - 448$

Step 1

Divide each term in $- 7 n^{2} = - 448$ by $- 7$ and simplify.

Divide each term in $- 7 n^{2} = - 448$ by $- 7$ .

$\frac{- 7 n^{2}}{- 7} = \frac{- 448}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 n^{2}}{- 7} = \frac{- 448}{- 7}$

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

$n^{2} = \frac{- 448}{- 7}$

Simplify the right side.

Divide $- 448$ by $- 7$ .

$n^{2} = 64$

Step 2

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

$n = \pm \sqrt{64}$

Step 3

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$n = \pm \sqrt{8^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$n = \pm 8$

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.

$n = 8$

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

$n = - 8$

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

$n = 8, - 8$