Solve Using the Quadratic Formula r^2=-624

$r^{2} = - 624$

Step 1

Add $624$ to both sides of the equation.

$r^{2} + 624 = 0$

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 $a = 1$ , $b = 0$ , and $c = 624$ into the quadratic formula and solve for $r$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot 624)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$r = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot 624}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 624$ .

Multiply $- 4$ by $1$ .

$r = \frac{0 \pm \sqrt{0 - 4 \cdot 624}}{2 \cdot 1}$

Multiply $- 4$ by $624$ .

$r = \frac{0 \pm \sqrt{0 - 2496}}{2 \cdot 1}$

Subtract $2496$ from $0$ .

$r = \frac{0 \pm \sqrt{- 2496}}{2 \cdot 1}$

Rewrite $- 2496$ as $- 1 (2496)$ .

$r = \frac{0 \pm \sqrt{- 1 \cdot 2496}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (2496)}$ as $\sqrt{- 1} \cdot \sqrt{2496}$ .

$r = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{2496}}{2 \cdot 1}$

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

$r = \frac{0 \pm i \cdot \sqrt{2496}}{2 \cdot 1}$

Rewrite $2496$ as $8^{2} \cdot 39$ .

Factor $64$ out of $2496$ .

$r = \frac{0 \pm i \cdot \sqrt{64 (39)}}{2 \cdot 1}$

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

$r = \frac{0 \pm i \cdot \sqrt{8^{2} \cdot 39}}{2 \cdot 1}$

Pull terms out from under the radical.

$r = \frac{0 \pm i \cdot (8 \sqrt{39})}{2 \cdot 1}$

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

$r = \frac{0 \pm 8 i \sqrt{39}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$r = \frac{0 \pm 8 i \sqrt{39}}{2}$

Simplify $\frac{0 \pm 8 i \sqrt{39}}{2}$ .

$r = \pm 4 i \sqrt{39}$