# How do you solve n^2-4=77?

Aug 4, 2016

$n = 9$

#### Explanation:

color(magenta)("Let's add 4 to both sides of the equation:"

${n}^{2} - \cancel{4} = 77$
$\textcolor{w h i t e}{a a} + \cancel{4}$ $\textcolor{w h i t e}{a} + 4$

On the left side of the equation you're left with ${n}^{2}$ since $\left(- 4\right) + \left(4\right) = 0.$ When 4 is added to 77 you obtain 81 on the right side:

${n}^{2} = 81$

Take the square root (since that is the inverse of squaring a number) on both sides of the equation to get n by itself:

$\sqrt{{n}^{2}} = \sqrt{81}$

Thus, $n = \pm 9$

The plus or minus symbol means that the answer can be positive 9 or negative 9.