Solve Using the Quadratic Formula 14x^2+42x+70=0

$14 x^{2} + 42 x + 70 = 0$

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 $a = 14$ , $b = 42$ , and $c = 70$ into the quadratic formula and solve for $x$ .

$\frac{- 42 \pm \sqrt{42^{2} - 4 \cdot (14 \cdot 70)}}{2 \cdot 14}$

Step 3

Simplify.

Simplify the numerator.

Raise $42$ to the power of $2$ .

$x = \frac{- 42 \pm \sqrt{1764 - 4 \cdot 14 \cdot 70}}{2 \cdot 14}$

Multiply $- 4 \cdot 14 \cdot 70$ .

Multiply $- 4$ by $14$ .

$x = \frac{- 42 \pm \sqrt{1764 - 56 \cdot 70}}{2 \cdot 14}$

Multiply $- 56$ by $70$ .

$x = \frac{- 42 \pm \sqrt{1764 - 3920}}{2 \cdot 14}$

Subtract $3920$ from $1764$ .

$x = \frac{- 42 \pm \sqrt{- 2156}}{2 \cdot 14}$

Rewrite $- 2156$ as $- 1 (2156)$ .

$x = \frac{- 42 \pm \sqrt{- 1 \cdot 2156}}{2 \cdot 14}$

Rewrite $\sqrt{- 1 (2156)}$ as $\sqrt{- 1} \cdot \sqrt{2156}$ .

$x = \frac{- 42 \pm \sqrt{- 1} \cdot \sqrt{2156}}{2 \cdot 14}$

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

$x = \frac{- 42 \pm i \cdot \sqrt{2156}}{2 \cdot 14}$

Rewrite $2156$ as $14^{2} \cdot 11$ .

Factor $196$ out of $2156$ .

$x = \frac{- 42 \pm i \cdot \sqrt{196 (11)}}{2 \cdot 14}$

Rewrite $196$ as $14^{2}$ .

$x = \frac{- 42 \pm i \cdot \sqrt{14^{2} \cdot 11}}{2 \cdot 14}$

Pull terms out from under the radical.

$x = \frac{- 42 \pm i \cdot (14 \sqrt{11})}{2 \cdot 14}$

Move $14$ to the left of $i$ .

$x = \frac{- 42 \pm 14 i \sqrt{11}}{2 \cdot 14}$

Multiply $2$ by $14$ .

$x = \frac{- 42 \pm 14 i \sqrt{11}}{28}$

Simplify $\frac{- 42 \pm 14 i \sqrt{11}}{28}$ .

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