Solve Using the Quadratic Formula x^2-8x-13=0

$x^{2} - 8 x - 13 = 0$

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 $a = 1$ , $b = - 8$ , and $c = - 13$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot - 13)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 13}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 13$ .

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 13}}{2 \cdot 1}$

Multiply $- 4$ by $- 13$ .

$x = \frac{8 \pm \sqrt{64 + 52}}{2 \cdot 1}$

Add $64$ and $52$ .

$x = \frac{8 \pm \sqrt{116}}{2 \cdot 1}$

Rewrite $116$ as $2^{2} \cdot 29$ .

Factor $4$ out of $116$ .

$x = \frac{8 \pm \sqrt{4 (29)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{8 \pm \sqrt{2^{2} \cdot 29}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{29}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 2 \sqrt{29}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{29}}{2}$ .

$x = 4 \pm \sqrt{29}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 4 \pm \sqrt{29}$

Decimal Form:

$x = 9.38516480 \dots, - 1.38516480 \dots$