Solve Using the Quadratic Formula 8x^2+32x+34=0

$8 x^{2} + 32 x + 34 = 0$

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 $a = 8$ , $b = 32$ , and $c = 34$ into the quadratic formula and solve for $x$ .

$\frac{- 32 \pm \sqrt{32^{2} - 4 \cdot (8 \cdot 34)}}{2 \cdot 8}$

Step 3

Simplify.

Simplify the numerator.

Raise $32$ to the power of $2$ .

$x = \frac{- 32 \pm \sqrt{1024 - 4 \cdot 8 \cdot 34}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot 34$ .

Multiply $- 4$ by $8$ .

$x = \frac{- 32 \pm \sqrt{1024 - 32 \cdot 34}}{2 \cdot 8}$

Multiply $- 32$ by $34$ .

$x = \frac{- 32 \pm \sqrt{1024 - 1088}}{2 \cdot 8}$

Subtract $1088$ from $1024$ .

$x = \frac{- 32 \pm \sqrt{- 64}}{2 \cdot 8}$

Rewrite $- 64$ as $- 1 (64)$ .

$x = \frac{- 32 \pm \sqrt{- 1 \cdot 64}}{2 \cdot 8}$

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$x = \frac{- 32 \pm \sqrt{- 1} \cdot \sqrt{64}}{2 \cdot 8}$

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

$x = \frac{- 32 \pm i \cdot \sqrt{64}}{2 \cdot 8}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{- 32 \pm i \cdot \sqrt{8^{2}}}{2 \cdot 8}$

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

$x = \frac{- 32 \pm i \cdot 8}{2 \cdot 8}$

Move $8$ to the left of $i$ .

$x = \frac{- 32 \pm 8 i}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{- 32 \pm 8 i}{16}$

Simplify $\frac{- 32 \pm 8 i}{16}$ .

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