Solve Using the Quadratic Formula 4a^2-45=0

$4 a^{2} - 45 = 0$

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 $a = 4$ , $b = 0$ , and $c = - 45$ into the quadratic formula and solve for $a$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $4$ .

$a = \frac{0 \pm \sqrt{0 - 16 \cdot - 45}}{2 \cdot 4}$

Multiply $- 16$ by $- 45$ .

$a = \frac{0 \pm \sqrt{0 + 720}}{2 \cdot 4}$

Add $0$ and $720$ .

$a = \frac{0 \pm \sqrt{720}}{2 \cdot 4}$

Rewrite $720$ as $12^{2} \cdot 5$ .

Factor $144$ out of $720$ .

$a = \frac{0 \pm \sqrt{144 (5)}}{2 \cdot 4}$

Rewrite $144$ as $12^{2}$ .

$a = \frac{0 \pm \sqrt{12^{2} \cdot 5}}{2 \cdot 4}$

Pull terms out from under the radical.

$a = \frac{0 \pm 12 \sqrt{5}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$a = \frac{0 \pm 12 \sqrt{5}}{8}$

Simplify $\frac{0 \pm 12 \sqrt{5}}{8}$ .

$a = \frac{\pm 3 \sqrt{5}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{\pm 3 \sqrt{5}}{2}$

Decimal Form:

$a = 3.35410196 \dots, - 3.35410196 \dots$