Solve Using the Quadratic Formula 2x^2-9x-221=0

$2 x^{2} - 9 x - 221 = 0$

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 $a = 2$ , $b = - 9$ , and $c = - 221$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (2 \cdot - 221)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 2 \cdot - 221}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 221$ .

Multiply $- 4$ by $2$ .

$x = \frac{9 \pm \sqrt{81 - 8 \cdot - 221}}{2 \cdot 2}$

Multiply $- 8$ by $- 221$ .

$x = \frac{9 \pm \sqrt{81 + 1768}}{2 \cdot 2}$

Add $81$ and $1768$ .

$x = \frac{9 \pm \sqrt{1849}}{2 \cdot 2}$

Rewrite $1849$ as $43^{2}$ .

$x = \frac{9 \pm \sqrt{43^{2}}}{2 \cdot 2}$

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

$x = \frac{9 \pm 43}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{9 \pm 43}{4}$

Step 4

The final answer is the combination of both solutions.

$x = 13, - \frac{17}{2}$