Solve Using the Quadratic Formula 2x^2-2x-24=0

$2 x^{2} - 2 x - 24 = 0$

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 $a = 2$ , $b = - 2$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (2 \cdot - 24)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 2$ to the power of $2$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 2 \cdot - 24}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 24$ .

Multiply $- 4$ by $2$ .

$x = \frac{2 \pm \sqrt{4 - 8 \cdot - 24}}{2 \cdot 2}$

Multiply $- 8$ by $- 24$ .

$x = \frac{2 \pm \sqrt{4 + 192}}{2 \cdot 2}$

Add $4$ and $192$ .

$x = \frac{2 \pm \sqrt{196}}{2 \cdot 2}$

Rewrite $196$ as $14^{2}$ .

$x = \frac{2 \pm \sqrt{14^{2}}}{2 \cdot 2}$

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

$x = \frac{2 \pm 14}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{2 \pm 14}{4}$

Simplify $\frac{2 \pm 14}{4}$ .

$x = \frac{1 \pm 7}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 4, - 3$