Solve Using the Quadratic Formula x^2-45=0

$x^{2} - 45 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 1$ , $b = 0$ , and $c = - 45$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 45}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 45$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 45}}{2 \cdot 1}$

Multiply $- 4$ by $- 45$ .

$x = \frac{0 \pm \sqrt{0 + 180}}{2 \cdot 1}$

Add $0$ and $180$ .

$x = \frac{0 \pm \sqrt{180}}{2 \cdot 1}$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$x = \frac{0 \pm \sqrt{36 (5)}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{0 \pm \sqrt{6^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm 6 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 6 \sqrt{5}}{2}$

Simplify $\frac{0 \pm 6 \sqrt{5}}{2}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 6.70820393 \dots, - 6.70820393 \dots$