Solve Using the Quadratic Formula 4x^2-52=0

$4 x^{2} - 52 = 0$

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 $c = - 52$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (4 \cdot - 52)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 4 \cdot - 52}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 52$ .

Multiply $- 4$ by $4$ .

$x = \frac{0 \pm \sqrt{0 - 16 \cdot - 52}}{2 \cdot 4}$

Multiply $- 16$ by $- 52$ .

$x = \frac{0 \pm \sqrt{0 + 832}}{2 \cdot 4}$

Add $0$ and $832$ .

$x = \frac{0 \pm \sqrt{832}}{2 \cdot 4}$

Rewrite $832$ as $8^{2} \cdot 13$ .

Factor $64$ out of $832$ .

$x = \frac{0 \pm \sqrt{64 (13)}}{2 \cdot 4}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{0 \pm \sqrt{8^{2} \cdot 13}}{2 \cdot 4}$

Pull terms out from under the radical.

$x = \frac{0 \pm 8 \sqrt{13}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{0 \pm 8 \sqrt{13}}{8}$

Simplify $\frac{0 \pm 8 \sqrt{13}}{8}$ .

$x = \pm \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{13}$

Decimal Form:

$x = 3.60555127 \dots, - 3.60555127 \dots$