Solve Using the Quadratic Formula 2x^2+8x+6=0

$2 x^{2} + 8 x + 6 = 0$

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 $a = 2$ , $b = 8$ , and $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (2 \cdot 6)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $8$ to the power of $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 2 \cdot 6}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 6$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 8 \cdot 6}}{2 \cdot 2}$

Multiply $- 8$ by $6$ .

$x = \frac{- 8 \pm \sqrt{64 - 48}}{2 \cdot 2}$

Subtract $48$ from $64$ .

$x = \frac{- 8 \pm \sqrt{16}}{2 \cdot 2}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{- 8 \pm \sqrt{4^{2}}}{2 \cdot 2}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 8 \pm 4}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 8 \pm 4}{4}$

Simplify $\frac{- 8 \pm 4}{4}$ .

$x = - 2 \pm 1$

Step 4

The final answer is the combination of both solutions.

$x = - 1, - 3$