Solve Using the Quadratic Formula 2x^2-x-28=0

$2 x^{2} - x - 28 = 0$

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 $a = 2$ , $b = - 1$ , and $c = - 28$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (2 \cdot - 28)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 2 \cdot - 28}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 28$ .

Multiply $- 4$ by $2$ .

$x = \frac{1 \pm \sqrt{1 - 8 \cdot - 28}}{2 \cdot 2}$

Multiply $- 8$ by $- 28$ .

$x = \frac{1 \pm \sqrt{1 + 224}}{2 \cdot 2}$

Add $1$ and $224$ .

$x = \frac{1 \pm \sqrt{225}}{2 \cdot 2}$

Rewrite $225$ as $15^{2}$ .

$x = \frac{1 \pm \sqrt{15^{2}}}{2 \cdot 2}$

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

$x = \frac{1 \pm 15}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{1 \pm 15}{4}$

Step 4

The final answer is the combination of both solutions.

$x = 4, - \frac{7}{2}$