Solve Using the Quadratic Formula -9=9x^2+2x

$- 9 = 9 x^{2} + 2 x$

Step 1

Move all the expressions to the left side of the equation.

Subtract $9 x^{2}$ from both sides of the equation.

$- 9 - 9 x^{2} = 2 x$

Subtract $2 x$ from both sides of the equation.

$- 9 - 9 x^{2} - 2 x = 0$

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 $a = - 9$ , $b = - 2$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

Raise $- 2$ to the power of $2$ .

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

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

Multiply $- 4$ by $- 9$ .

$x = \frac{2 \pm \sqrt{4 + 36 \cdot - 9}}{2 \cdot - 9}$

Multiply $36$ by $- 9$ .

$x = \frac{2 \pm \sqrt{4 - 324}}{2 \cdot - 9}$

Subtract $324$ from $4$ .

$x = \frac{2 \pm \sqrt{- 320}}{2 \cdot - 9}$

Rewrite $- 320$ as $- 1 (320)$ .

$x = \frac{2 \pm \sqrt{- 1 \cdot 320}}{2 \cdot - 9}$

Rewrite $\sqrt{- 1 (320)}$ as $\sqrt{- 1} \cdot \sqrt{320}$ .

$x = \frac{2 \pm \sqrt{- 1} \cdot \sqrt{320}}{2 \cdot - 9}$

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

$x = \frac{2 \pm i \cdot \sqrt{320}}{2 \cdot - 9}$

Rewrite $320$ as $8^{2} \cdot 5$ .

Factor $64$ out of $320$ .

$x = \frac{2 \pm i \cdot \sqrt{64 (5)}}{2 \cdot - 9}$

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

$x = \frac{2 \pm i \cdot \sqrt{8^{2} \cdot 5}}{2 \cdot - 9}$

Pull terms out from under the radical.

$x = \frac{2 \pm i \cdot (8 \sqrt{5})}{2 \cdot - 9}$

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

$x = \frac{2 \pm 8 i \sqrt{5}}{2 \cdot - 9}$

Multiply $2$ by $- 9$ .

$x = \frac{2 \pm 8 i \sqrt{5}}{- 18}$

Simplify $\frac{2 \pm 8 i \sqrt{5}}{- 18}$ .

$x = \frac{1 \pm 4 i \sqrt{5}}{- 9}$

Move the negative in front of the fraction.

$x = - \frac{1 \pm 4 i \sqrt{5}}{9}$

Solve Using the Quadratic Formula -9=9x^2+2x

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