Solve Using the Quadratic Formula 11x^2-4x=-2

$11 x^{2} - 4 x = - 2$

Add $2$ to both sides of the equation.

$11 x^{2} - 4 x + 2 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 11$ , $b = - 4$ , and $c = 2$ into the quadratic formula and solve for $x$ .

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

Simplify.

Simplify the numerator.

Raise $- 4$ to the power of $2$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 11 \cdot 2}}{2 \cdot 11}$

Multiply $- 4$ by $11$ .

$x = \frac{4 \pm \sqrt{16 - 44 \cdot 2}}{2 \cdot 11}$

Multiply $- 44$ by $2$ .

$x = \frac{4 \pm \sqrt{16 - 88}}{2 \cdot 11}$

Subtract $88$ from $16$ .

$x = \frac{4 \pm \sqrt{- 72}}{2 \cdot 11}$

Rewrite $- 72$ as $- 1 (72)$ .

$x = \frac{4 \pm \sqrt{- 1 \cdot 72}}{2 \cdot 11}$

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$x = \frac{4 \pm \sqrt{- 1} \cdot \sqrt{72}}{2 \cdot 11}$

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

$x = \frac{4 \pm i \cdot \sqrt{72}}{2 \cdot 11}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$x = \frac{4 \pm i \cdot \sqrt{36 (2)}}{2 \cdot 11}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{4 \pm i \cdot \sqrt{6^{2} \cdot 2}}{2 \cdot 11}$

Pull terms out from under the radical.

$x = \frac{4 \pm i \cdot (6 \sqrt{2})}{2 \cdot 11}$

Move $6$ to the left of $i$ .

$x = \frac{4 \pm 6 i \sqrt{2}}{2 \cdot 11}$

Multiply $2$ by $11$ .

$x = \frac{4 \pm 6 i \sqrt{2}}{22}$

Simplify $\frac{4 \pm 6 i \sqrt{2}}{22}$ .

$x = \frac{2 \pm 3 i \sqrt{2}}{11}$