Solve Using the Quadratic Formula x^2+8x-15=0

$x^{2} + 8 x - 15 = 0$

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 $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (1 \cdot - 15)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 15}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 15$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot - 15}}{2 \cdot 1}$

Multiply $- 4$ by $- 15$ .

$x = \frac{- 8 \pm \sqrt{64 + 60}}{2 \cdot 1}$

Add $64$ and $60$ .

$x = \frac{- 8 \pm \sqrt{124}}{2 \cdot 1}$

Rewrite $124$ as $2^{2} \cdot 31$ .

Factor $4$ out of $124$ .

$x = \frac{- 8 \pm \sqrt{4 (31)}}{2 \cdot 1}$

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

$x = \frac{- 8 \pm \sqrt{2^{2} \cdot 31}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 8 \pm 2 \sqrt{31}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 8 \pm 2 \sqrt{31}}{2}$

Simplify $\frac{- 8 \pm 2 \sqrt{31}}{2}$ .

$x = - 4 \pm \sqrt{31}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 4 \pm \sqrt{31}$

Decimal Form:

$x = 1.56776436 \dots, - 9.56776436 \dots$