Solve Using the Quadratic Formula -m^2-6m-20=0

$- m^{2} - 6 m - 20 = 0$

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 $a = - 1$ , $b = - 6$ , and $c = - 20$ into the quadratic formula and solve for $m$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (- 1 \cdot - 20)}}{2 \cdot - 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$m = \frac{6 \pm \sqrt{36 - 4 \cdot - 1 \cdot - 20}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot - 20$ .

Multiply $- 4$ by $- 1$ .

$m = \frac{6 \pm \sqrt{36 + 4 \cdot - 20}}{2 \cdot - 1}$

Multiply $4$ by $- 20$ .

$m = \frac{6 \pm \sqrt{36 - 80}}{2 \cdot - 1}$

Subtract $80$ from $36$ .

$m = \frac{6 \pm \sqrt{- 44}}{2 \cdot - 1}$

Rewrite $- 44$ as $- 1 (44)$ .

$m = \frac{6 \pm \sqrt{- 1 \cdot 44}}{2 \cdot - 1}$

Rewrite $\sqrt{- 1 (44)}$ as $\sqrt{- 1} \cdot \sqrt{44}$ .

$m = \frac{6 \pm \sqrt{- 1} \cdot \sqrt{44}}{2 \cdot - 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$m = \frac{6 \pm i \cdot \sqrt{44}}{2 \cdot - 1}$

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$m = \frac{6 \pm i \cdot \sqrt{4 (11)}}{2 \cdot - 1}$

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

$m = \frac{6 \pm i \cdot \sqrt{2^{2} \cdot 11}}{2 \cdot - 1}$

Pull terms out from under the radical.

$m = \frac{6 \pm i \cdot (2 \sqrt{11})}{2 \cdot - 1}$

Move $2$ to the left of $i$ .

$m = \frac{6 \pm 2 i \sqrt{11}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$m = \frac{6 \pm 2 i \sqrt{11}}{- 2}$

Simplify $\frac{6 \pm 2 i \sqrt{11}}{- 2}$ .

$m = \frac{3 \pm i \sqrt{11}}{- 1}$

Move the negative one from the denominator of $\frac{3 \pm i \sqrt{11}}{- 1}$ .

$m = - 1 \cdot (3 \pm i \sqrt{11})$

Rewrite $- 1 \cdot (3 \pm i \sqrt{11})$ as $- (3 \pm i \sqrt{11})$ .

$m = - (3 \pm i \sqrt{11})$