Solve Using the Quadratic Formula 8x^2+7x=-2

$8 x^{2} + 7 x = - 2$

Step 1

Add $2$ to both sides of the equation.

$8 x^{2} + 7 x + 2 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 8$ , $b = 7$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (8 \cdot 2)}}{2 \cdot 8}$

Step 4

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 8 \cdot 2}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot 2$ .

Multiply $- 4$ by $8$ .

$x = \frac{- 7 \pm \sqrt{49 - 32 \cdot 2}}{2 \cdot 8}$

Multiply $- 32$ by $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 64}}{2 \cdot 8}$

Subtract $64$ from $49$ .

$x = \frac{- 7 \pm \sqrt{- 15}}{2 \cdot 8}$

Rewrite $- 15$ as $- 1 (15)$ .

$x = \frac{- 7 \pm \sqrt{- 1 \cdot 15}}{2 \cdot 8}$

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$x = \frac{- 7 \pm \sqrt{- 1} \cdot \sqrt{15}}{2 \cdot 8}$

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

$x = \frac{- 7 \pm i \sqrt{15}}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{- 7 \pm i \sqrt{15}}{16}$