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

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

Step 1

Add $2$ to both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 7 \cdot 2}}{2 \cdot 7}$

Multiply $- 4 \cdot 7 \cdot 2$ .

Multiply $- 4$ by $7$ .

$x = \frac{- 8 \pm \sqrt{64 - 28 \cdot 2}}{2 \cdot 7}$

Multiply $- 28$ by $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 56}}{2 \cdot 7}$

Subtract $56$ from $64$ .

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

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $7$ .

$x = \frac{- 8 \pm 2 \sqrt{2}}{14}$

Simplify $\frac{- 8 \pm 2 \sqrt{2}}{14}$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.36939806 \dots, - 0.77345908 \dots$