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

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

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 $a = 1$ , $b = 15$ , and $c = 8$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

Raise $15$ to the power of $2$ .

$x = \frac{- 15 \pm \sqrt{225 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 8$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 15 \pm \sqrt{225 - 4 \cdot 8}}{2 \cdot 1}$

Multiply $- 4$ by $8$ .

$x = \frac{- 15 \pm \sqrt{225 - 32}}{2 \cdot 1}$

Subtract $32$ from $225$ .

$x = \frac{- 15 \pm \sqrt{193}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 15 \pm \sqrt{193}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 15 \pm \sqrt{193}}{2}$

Decimal Form:

$x = - 0.55377800 \dots, - 14.44622199 \dots$