# How do you solve -7n^2=-448?

Sep 1, 2016

$n = \pm 8$

#### Explanation:

Divide both sides by -7 so as to isolate the ${n}^{2}$ term.

$\frac{{\cancel{- 7}}^{1} {n}^{2}}{\cancel{- 7}} ^ 1 = \frac{{\cancel{- 448}}^{64}}{\cancel{- 7}} ^ 1 \Rightarrow {n}^{2} = 64$

now take the square root of both sides

$\sqrt{{n}^{2}} = \pm \sqrt{64} \Rightarrow n = \pm 8$

Sep 1, 2016

$n = 8 \mathmr{and} n = - 8$

#### Explanation:

This is a quadratic equation, it can be solved by factorising.

$- 7 {n}^{2} = - 448 \leftarrow \div \text{ } - 7$ to simplify. Divide on both sides.

${n}^{2} = 64 \leftarrow$ make it =0

${n}^{2} - 64 \leftarrow$ difference of two squares.

$\left(n + 8\right) \left(n - 8\right) = 0$

Either factor can be equal to 0.

If $n + 8 = 0 \rightarrow n = - 8$

If $n - 8 = 0 \rightarrow n = 8$