Find All Complex Solutions 14x^2-11x+10=0

$14 x^{2} - 11 x + 10 = 0$

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 $a = 14$ , $b = - 11$ , and $c = 10$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (14 \cdot 10)}}{2 \cdot 14}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 14 \cdot 10}}{2 \cdot 14}$

Multiply $- 4 \cdot 14 \cdot 10$ .

Multiply $- 4$ by $14$ .

$x = \frac{11 \pm \sqrt{121 - 56 \cdot 10}}{2 \cdot 14}$

Multiply $- 56$ by $10$ .

$x = \frac{11 \pm \sqrt{121 - 560}}{2 \cdot 14}$

Subtract $560$ from $121$ .

$x = \frac{11 \pm \sqrt{- 439}}{2 \cdot 14}$

Rewrite $- 439$ as $- 1 (439)$ .

$x = \frac{11 \pm \sqrt{- 1 \cdot 439}}{2 \cdot 14}$

Rewrite $\sqrt{- 1 (439)}$ as $\sqrt{- 1} \cdot \sqrt{439}$ .

$x = \frac{11 \pm \sqrt{- 1} \cdot \sqrt{439}}{2 \cdot 14}$

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

$x = \frac{11 \pm i \sqrt{439}}{2 \cdot 14}$

Multiply $2$ by $14$ .

$x = \frac{11 \pm i \sqrt{439}}{28}$