Solve Using the Quadratic Formula 2x^2-50=0

$2 x^{2} - 50 = 0$

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 $a = 2$ , $b = 0$ , and $c = - 50$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (2 \cdot - 50)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 2 \cdot - 50}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 50$ .

Multiply $- 4$ by $2$ .

$x = \frac{0 \pm \sqrt{0 - 8 \cdot - 50}}{2 \cdot 2}$

Multiply $- 8$ by $- 50$ .

$x = \frac{0 \pm \sqrt{0 + 400}}{2 \cdot 2}$

Add $0$ and $400$ .

$x = \frac{0 \pm \sqrt{400}}{2 \cdot 2}$

Rewrite $400$ as $20^{2}$ .

$x = \frac{0 \pm \sqrt{20^{2}}}{2 \cdot 2}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm 20}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{0 \pm 20}{4}$

Simplify $\frac{0 \pm 20}{4}$ .

$x = \pm 5$

Step 4

The final answer is the combination of both solutions.

$x = 5, - 5$