Solve Using the Quadratic Formula 2x^2+8x+3=0

$2 x^{2} + 8 x + 3 = 0$

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 $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (2 \cdot 3)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 2 \cdot 3}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 3$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 8 \cdot 3}}{2 \cdot 2}$

Multiply $- 8$ by $3$ .

$x = \frac{- 8 \pm \sqrt{64 - 24}}{2 \cdot 2}$

Subtract $24$ from $64$ .

$x = \frac{- 8 \pm \sqrt{40}}{2 \cdot 2}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$x = \frac{- 8 \pm \sqrt{4 (10)}}{2 \cdot 2}$

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

$x = \frac{- 8 \pm \sqrt{2^{2} \cdot 10}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 8 \pm 2 \sqrt{10}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 8 \pm 2 \sqrt{10}}{4}$

Simplify $\frac{- 8 \pm 2 \sqrt{10}}{4}$ .

$x = \frac{- 4 \pm \sqrt{10}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 4 \pm \sqrt{10}}{2}$

Decimal Form:

$x = - 0.41886116 \dots, - 3.58113883 \dots$