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

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

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 $a = 8$ , $b = - 1$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (8 \cdot 8)}}{2 \cdot 8}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 8 \cdot 8}}{2 \cdot 8}$

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

Multiply $- 4$ by $8$ .

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

Multiply $- 32$ by $8$ .

$x = \frac{1 \pm \sqrt{1 - 256}}{2 \cdot 8}$

Subtract $256$ from $1$ .

$x = \frac{1 \pm \sqrt{- 255}}{2 \cdot 8}$

Rewrite $- 255$ as $- 1 (255)$ .

$x = \frac{1 \pm \sqrt{- 1 \cdot 255}}{2 \cdot 8}$

Rewrite $\sqrt{- 1 (255)}$ as $\sqrt{- 1} \cdot \sqrt{255}$ .

$x = \frac{1 \pm \sqrt{- 1} \cdot \sqrt{255}}{2 \cdot 8}$

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

$x = \frac{1 \pm i \sqrt{255}}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{1 \pm i \sqrt{255}}{16}$