# How do you solve x^2 - 45 = 0 using the quadratic formula?

Jul 15, 2017

See a solution process below:

#### Explanation:

To solve this problem using the quadratic formula we can rewrite the equation as:

$1 {x}^{2} + 0 x - 45 = 0$

The quadratic formula states:

For $a {x}^{2} + b x + c = 0$, the values of $x$ which are the solutions to the equation are given by:

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

Substituting $1$ for $a$; $0$ for $b$ and $- 45$ for $c$ gives:

$x = \frac{- 0 \pm \sqrt{{0}^{2} - \left(4 \cdot 1 \cdot - 45\right)}}{2 \cdot 1}$

$x = \pm \frac{\sqrt{0 - \left(- 180\right)}}{2}$

$x = \pm \frac{\sqrt{180}}{2}$

$x = \pm \frac{\sqrt{36 \cdot 5}}{2}$

$x = \pm \frac{\sqrt{36} \cdot \sqrt{5}}{2}$

$x = \pm \frac{6 \sqrt{5}}{2}$

$x = \pm 3 \sqrt{5}$