# How do you solve n^2 - 17=64 using the quadratic formula?

Aug 5, 2016

$n = \pm 9$

#### Explanation:

${n}^{2} - 17 = 64$
${n}^{2} = 64 + 17$
${n}^{2} = 81$
$n = \sqrt{81}$
$n = \pm 9$

Aug 5, 2016

$n = \pm 9$

#### Explanation:

Write as ${n}^{2} - 81$

As it is insisted we use the quadratic formula write as:

${n}^{2} + 0 n - 81 = 0$

$\implies n = \frac{- 0 \pm \sqrt{{0}^{2} - 4 \left(1\right) \left(- 81\right)}}{2 \left(1\right)}$

$\implies n = \pm \frac{\sqrt{324}}{2} = \frac{\pm 18}{2} = \pm 9$

Aug 5, 2016

$n = 9 , - 9$

#### Explanation:

${n}^{2} - 17 = 64$

Subtract $64$ from both sides of the equation.

${n}^{2} - 17 - 64 = 0$

Simplify.

${n}^{2} - 81$

This equation is in the form of a quadratic equation, $a {x}^{2} + b x + c = 0$, where $a = 1$, $b = 0$, and $c = - 81$.

The quadratic formula can be used to solve this quadratic equation.

$x = \frac{- {b}^{2} \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Substitute $n$ for $x$ and plug the known values into the formula.

$n = \frac{- 0 \pm \sqrt{{0}^{2} - 4 \cdot 1 \cdot - 81}}{2 \cdot 1}$

Simplify.

$n = \frac{\pm \sqrt{324}}{2}$

Simplify.

$n = \pm \frac{18}{2}$

Simplify.

$n = \pm 9$

Solve for $n$.

$n = 9$

$n = - 9$