Solve Using the Quadratic Formula 2x^2-13x-2=0

$2 x^{2} - 13 x - 2 = 0$

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 $a = 2$ , $b = - 13$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{13 \pm \sqrt{{(- 13)}^{2} - 4 \cdot (2 \cdot - 2)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 13$ to the power of $2$ .

$x = \frac{13 \pm \sqrt{169 - 4 \cdot 2 \cdot - 2}}{2 \cdot 2}$

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

Multiply $- 4$ by $2$ .

$x = \frac{13 \pm \sqrt{169 - 8 \cdot - 2}}{2 \cdot 2}$

Multiply $- 8$ by $- 2$ .

$x = \frac{13 \pm \sqrt{169 + 16}}{2 \cdot 2}$

Add $169$ and $16$ .

$x = \frac{13 \pm \sqrt{185}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{13 \pm \sqrt{185}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13 \pm \sqrt{185}}{4}$

Decimal Form:

$x = 6.65036762 \dots, - 0.15036762 \dots$