Solve Using the Quadratic Formula x^2+15x=-56

$x^{2} + 15 x = - 56$

Step 1

Add $56$ to both sides of the equation.

$x^{2} + 15 x + 56 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 15$ , and $c = 56$ into the quadratic formula and solve for $x$ .

$\frac{- 15 \pm \sqrt{15^{2} - 4 \cdot (1 \cdot 56)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 15 \pm \sqrt{225 - 4 \cdot 1 \cdot 56}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 56$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 15 \pm \sqrt{225 - 4 \cdot 56}}{2 \cdot 1}$

Multiply $- 4$ by $56$ .

$x = \frac{- 15 \pm \sqrt{225 - 224}}{2 \cdot 1}$

Subtract $224$ from $225$ .

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

Any root of $1$ is $1$ .

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

Multiply $2$ by $1$ .

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

Step 5

The final answer is the combination of both solutions.

$x = - 7, - 8$