Solve Using the Quadratic Formula -11x^2+2x=10

$- 11 x^{2} + 2 x = 10$

Step 1

Subtract $10$ from both sides of the equation.

$- 11 x^{2} + 2 x - 10 = 0$

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 $a = - 11$ , $b = 2$ , and $c = - 10$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (- 11 \cdot - 10)}}{2 \cdot - 11}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot - 11 \cdot - 10}}{2 \cdot - 11}$

Multiply $- 4 \cdot - 11 \cdot - 10$ .

Multiply $- 4$ by $- 11$ .

$x = \frac{- 2 \pm \sqrt{4 + 44 \cdot - 10}}{2 \cdot - 11}$

Multiply $44$ by $- 10$ .

$x = \frac{- 2 \pm \sqrt{4 - 440}}{2 \cdot - 11}$

Subtract $440$ from $4$ .

$x = \frac{- 2 \pm \sqrt{- 436}}{2 \cdot - 11}$

Rewrite $- 436$ as $- 1 (436)$ .

$x = \frac{- 2 \pm \sqrt{- 1 \cdot 436}}{2 \cdot - 11}$

Rewrite $\sqrt{- 1 (436)}$ as $\sqrt{- 1} \cdot \sqrt{436}$ .

$x = \frac{- 2 \pm \sqrt{- 1} \cdot \sqrt{436}}{2 \cdot - 11}$

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

$x = \frac{- 2 \pm i \cdot \sqrt{436}}{2 \cdot - 11}$

Rewrite $436$ as $2^{2} \cdot 109$ .

Factor $4$ out of $436$ .

$x = \frac{- 2 \pm i \cdot \sqrt{4 (109)}}{2 \cdot - 11}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 2 \pm i \cdot \sqrt{2^{2} \cdot 109}}{2 \cdot - 11}$

Pull terms out from under the radical.

$x = \frac{- 2 \pm i \cdot (2 \sqrt{109})}{2 \cdot - 11}$

Move $2$ to the left of $i$ .

$x = \frac{- 2 \pm 2 i \sqrt{109}}{2 \cdot - 11}$

Multiply $2$ by $- 11$ .

$x = \frac{- 2 \pm 2 i \sqrt{109}}{- 22}$

Simplify $\frac{- 2 \pm 2 i \sqrt{109}}{- 22}$ .

$x = \frac{1 \pm i \sqrt{109}}{11}$