Solve Using the Quadratic Formula 9x^2+16=0

$9 x^{2} + 16 = 0$

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 $a = 9$ , $b = 0$ , and $c = 16$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (9 \cdot 16)}}{2 \cdot 9}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 9 \cdot 16}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot 16$ .

Multiply $- 4$ by $9$ .

$x = \frac{0 \pm \sqrt{0 - 36 \cdot 16}}{2 \cdot 9}$

Multiply $- 36$ by $16$ .

$x = \frac{0 \pm \sqrt{0 - 576}}{2 \cdot 9}$

Subtract $576$ from $0$ .

$x = \frac{0 \pm \sqrt{- 576}}{2 \cdot 9}$

Rewrite $- 576$ as $- 1 (576)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 576}}{2 \cdot 9}$

Rewrite $\sqrt{- 1 (576)}$ as $\sqrt{- 1} \cdot \sqrt{576}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{576}}{2 \cdot 9}$

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

$x = \frac{0 \pm i \cdot \sqrt{576}}{2 \cdot 9}$

Rewrite $576$ as $24^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{24^{2}}}{2 \cdot 9}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm i \cdot 24}{2 \cdot 9}$

Move $24$ to the left of $i$ .

$x = \frac{0 \pm 24 i}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{0 \pm 24 i}{18}$

Simplify $\frac{0 \pm 24 i}{18}$ .

$x = \frac{\pm 4 i}{3}$