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

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

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

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $16$ .

$x = \frac{0 \pm \sqrt{0 - 64 \cdot 9}}{2 \cdot 16}$

Multiply $- 64$ by $9$ .

$x = \frac{0 \pm \sqrt{0 - 576}}{2 \cdot 16}$

Subtract $576$ from $0$ .

$x = \frac{0 \pm \sqrt{- 576}}{2 \cdot 16}$

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

$x = \frac{0 \pm \sqrt{- 1 \cdot 576}}{2 \cdot 16}$

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

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{576}}{2 \cdot 16}$

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

$x = \frac{0 \pm i \cdot \sqrt{576}}{2 \cdot 16}$

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

$x = \frac{0 \pm i \cdot \sqrt{24^{2}}}{2 \cdot 16}$

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

$x = \frac{0 \pm i \cdot 24}{2 \cdot 16}$

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

$x = \frac{0 \pm 24 i}{2 \cdot 16}$

Multiply $2$ by $16$ .

$x = \frac{0 \pm 24 i}{32}$

Simplify $\frac{0 \pm 24 i}{32}$ .

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