Solve Using the Quadratic Formula 8x^2-48=0

$8 x^{2} - 48 = 0$

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 $a = 8$ , $b = 0$ , and $c = - 48$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (8 \cdot - 48)}}{2 \cdot 8}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 8 \cdot - 48}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot - 48$ .

Multiply $- 4$ by $8$ .

$x = \frac{0 \pm \sqrt{0 - 32 \cdot - 48}}{2 \cdot 8}$

Multiply $- 32$ by $- 48$ .

$x = \frac{0 \pm \sqrt{0 + 1536}}{2 \cdot 8}$

Add $0$ and $1536$ .

$x = \frac{0 \pm \sqrt{1536}}{2 \cdot 8}$

Rewrite $1536$ as $16^{2} \cdot 6$ .

Factor $256$ out of $1536$ .

$x = \frac{0 \pm \sqrt{256 (6)}}{2 \cdot 8}$

Rewrite $256$ as $16^{2}$ .

$x = \frac{0 \pm \sqrt{16^{2} \cdot 6}}{2 \cdot 8}$

Pull terms out from under the radical.

$x = \frac{0 \pm 16 \sqrt{6}}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{0 \pm 16 \sqrt{6}}{16}$

Simplify $\frac{0 \pm 16 \sqrt{6}}{16}$ .

$x = \pm \sqrt{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{6}$

Decimal Form:

$x = 2.44948974 \dots, - 2.44948974 \dots$