Solve Using the Quadratic Formula 4m^2+76=0

$4 m^{2} + 76 = 0$

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 $a = 4$ , $b = 0$ , and $c = 76$ into the quadratic formula and solve for $m$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (4 \cdot 76)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$m = \frac{0 \pm \sqrt{0 - 4 \cdot 4 \cdot 76}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot 76$ .

Multiply $- 4$ by $4$ .

$m = \frac{0 \pm \sqrt{0 - 16 \cdot 76}}{2 \cdot 4}$

Multiply $- 16$ by $76$ .

$m = \frac{0 \pm \sqrt{0 - 1216}}{2 \cdot 4}$

Subtract $1216$ from $0$ .

$m = \frac{0 \pm \sqrt{- 1216}}{2 \cdot 4}$

Rewrite $- 1216$ as $- 1 (1216)$ .

$m = \frac{0 \pm \sqrt{- 1 \cdot 1216}}{2 \cdot 4}$

Rewrite $\sqrt{- 1 (1216)}$ as $\sqrt{- 1} \cdot \sqrt{1216}$ .

$m = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{1216}}{2 \cdot 4}$

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

$m = \frac{0 \pm i \cdot \sqrt{1216}}{2 \cdot 4}$

Rewrite $1216$ as $8^{2} \cdot 19$ .

Factor $64$ out of $1216$ .

$m = \frac{0 \pm i \cdot \sqrt{64 (19)}}{2 \cdot 4}$

Rewrite $64$ as $8^{2}$ .

$m = \frac{0 \pm i \cdot \sqrt{8^{2} \cdot 19}}{2 \cdot 4}$

Pull terms out from under the radical.

$m = \frac{0 \pm i \cdot (8 \sqrt{19})}{2 \cdot 4}$

Move $8$ to the left of $i$ .

$m = \frac{0 \pm 8 i \sqrt{19}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$m = \frac{0 \pm 8 i \sqrt{19}}{8}$

Simplify $\frac{0 \pm 8 i \sqrt{19}}{8}$ .

$m = \pm i \sqrt{19}$