Solve Using the Quadratic Formula x^2=-7x-8

$x^{2} = - 7 x - 8$

Step 1

Move all the expressions to the left side of the equation.

Add $7 x$ to both sides of the equation.

$x^{2} + 7 x = - 8$

Add $8$ to both sides of the equation.

$x^{2} + 7 x + 8 = 0$

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 $a = 1$ , $b = 7$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot 8)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 8}}{2 \cdot 1}$

Multiply $- 4$ by $8$ .

$x = \frac{- 7 \pm \sqrt{49 - 32}}{2 \cdot 1}$

Subtract $32$ from $49$ .

$x = \frac{- 7 \pm \sqrt{17}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm \sqrt{17}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 7 \pm \sqrt{17}}{2}$

Decimal Form:

$x = - 1.43844718 \dots, - 5.56155281 \dots$