Solve for m m^2+8m=-3

$m^{2} + 8 m = - 3$

Step 1

Add $3$ to both sides of the equation.

$m^{2} + 8 m + 3 = 0$

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 $a = 1$ , $b = 8$ , and $c = 3$ into the quadratic formula and solve for $m$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (1 \cdot 3)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$m = \frac{- 8 \pm \sqrt{64 - 4 \cdot 1 \cdot 3}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 3$ .

Multiply $- 4$ by $1$ .

$m = \frac{- 8 \pm \sqrt{64 - 4 \cdot 3}}{2 \cdot 1}$

Multiply $- 4$ by $3$ .

$m = \frac{- 8 \pm \sqrt{64 - 12}}{2 \cdot 1}$

Subtract $12$ from $64$ .

$m = \frac{- 8 \pm \sqrt{52}}{2 \cdot 1}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

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

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

$m = \frac{- 8 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot 1}$

Pull terms out from under the radical.

$m = \frac{- 8 \pm 2 \sqrt{13}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$m = \frac{- 8 \pm 2 \sqrt{13}}{2}$

Simplify $\frac{- 8 \pm 2 \sqrt{13}}{2}$ .

$m = - 4 \pm \sqrt{13}$

Step 5

The final answer is the combination of both solutions.

$m = - 4 + \sqrt{13}, - 4 - \sqrt{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = - 4 + \sqrt{13}, - 4 - \sqrt{13}$

Decimal Form:

$m = - 0.39444872 \dots, - 7.60555127 \dots$