Solve Using the Quadratic Formula x^2+9x^2+20=0

$x^{2} + 9 x^{2} + 20 = 0$

Step 1

Simplify the left side.

Add $x^{2}$ and $9 x^{2}$ .

$10 x^{2} + 20 = 0$

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 $a = 10$ , $b = 0$ , and $c = 20$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (10 \cdot 20)}}{2 \cdot 10}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 10 \cdot 20}}{2 \cdot 10}$

Multiply $- 4 \cdot 10 \cdot 20$ .

Multiply $- 4$ by $10$ .

$x = \frac{0 \pm \sqrt{0 - 40 \cdot 20}}{2 \cdot 10}$

Multiply $- 40$ by $20$ .

$x = \frac{0 \pm \sqrt{0 - 800}}{2 \cdot 10}$

Subtract $800$ from $0$ .

$x = \frac{0 \pm \sqrt{- 800}}{2 \cdot 10}$

Rewrite $- 800$ as $- 1 (800)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 800}}{2 \cdot 10}$

Rewrite $\sqrt{- 1 (800)}$ as $\sqrt{- 1} \cdot \sqrt{800}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{800}}{2 \cdot 10}$

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

$x = \frac{0 \pm i \cdot \sqrt{800}}{2 \cdot 10}$

Rewrite $800$ as $20^{2} \cdot 2$ .

Factor $400$ out of $800$ .

$x = \frac{0 \pm i \cdot \sqrt{400 (2)}}{2 \cdot 10}$

Rewrite $400$ as $20^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{20^{2} \cdot 2}}{2 \cdot 10}$

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (20 \sqrt{2})}{2 \cdot 10}$

Move $20$ to the left of $i$ .

$x = \frac{0 \pm 20 i \sqrt{2}}{2 \cdot 10}$

Multiply $2$ by $10$ .

$x = \frac{0 \pm 20 i \sqrt{2}}{20}$

Simplify $\frac{0 \pm 20 i \sqrt{2}}{20}$ .

$x = \pm i \sqrt{2}$