Solve Using the Quadratic Formula 2x^2+26x+156=0

$2 x^{2} + 26 x + 156 = 0$

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 $a = 2$ , $b = 26$ , and $c = 156$ into the quadratic formula and solve for $x$ .

$\frac{- 26 \pm \sqrt{26^{2} - 4 \cdot (2 \cdot 156)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $26$ to the power of $2$ .

$x = \frac{- 26 \pm \sqrt{676 - 4 \cdot 2 \cdot 156}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 156$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 26 \pm \sqrt{676 - 8 \cdot 156}}{2 \cdot 2}$

Multiply $- 8$ by $156$ .

$x = \frac{- 26 \pm \sqrt{676 - 1248}}{2 \cdot 2}$

Subtract $1248$ from $676$ .

$x = \frac{- 26 \pm \sqrt{- 572}}{2 \cdot 2}$

Rewrite $- 572$ as $- 1 (572)$ .

$x = \frac{- 26 \pm \sqrt{- 1 \cdot 572}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (572)}$ as $\sqrt{- 1} \cdot \sqrt{572}$ .

$x = \frac{- 26 \pm \sqrt{- 1} \cdot \sqrt{572}}{2 \cdot 2}$

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

$x = \frac{- 26 \pm i \cdot \sqrt{572}}{2 \cdot 2}$

Rewrite $572$ as $2^{2} \cdot 143$ .

Factor $4$ out of $572$ .

$x = \frac{- 26 \pm i \cdot \sqrt{4 (143)}}{2 \cdot 2}$

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

$x = \frac{- 26 \pm i \cdot \sqrt{2^{2} \cdot 143}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 26 \pm i \cdot (2 \sqrt{143})}{2 \cdot 2}$

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

$x = \frac{- 26 \pm 2 i \sqrt{143}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 26 \pm 2 i \sqrt{143}}{4}$

Simplify $\frac{- 26 \pm 2 i \sqrt{143}}{4}$ .

$x = \frac{- 13 \pm i \sqrt{143}}{2}$