Find All Complex Solutions 100x^2+81=0

$100 x^{2} + 81 = 0$

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 $a = 100$ , $b = 0$ , and $c = 81$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (100 \cdot 81)}}{2 \cdot 100}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 100 \cdot 81}}{2 \cdot 100}$

Multiply $- 4 \cdot 100 \cdot 81$ .

Multiply $- 4$ by $100$ .

$x = \frac{0 \pm \sqrt{0 - 400 \cdot 81}}{2 \cdot 100}$

Multiply $- 400$ by $81$ .

$x = \frac{0 \pm \sqrt{0 - 32400}}{2 \cdot 100}$

Subtract $32400$ from $0$ .

$x = \frac{0 \pm \sqrt{- 32400}}{2 \cdot 100}$

Rewrite $- 32400$ as $- 1 (32400)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 32400}}{2 \cdot 100}$

Rewrite $\sqrt{- 1 (32400)}$ as $\sqrt{- 1} \cdot \sqrt{32400}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{32400}}{2 \cdot 100}$

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

$x = \frac{0 \pm i \cdot \sqrt{32400}}{2 \cdot 100}$

Rewrite $32400$ as $180^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{180^{2}}}{2 \cdot 100}$

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

$x = \frac{0 \pm i \cdot 180}{2 \cdot 100}$

Move $180$ to the left of $i$ .

$x = \frac{0 \pm 180 i}{2 \cdot 100}$

Multiply $2$ by $100$ .

$x = \frac{0 \pm 180 i}{200}$

Simplify $\frac{0 \pm 180 i}{200}$ .

$x = \frac{\pm 9 i}{10}$