Solve Using the Quadratic Formula -7x^2+7x+1=-8

$- 7 x^{2} + 7 x + 1 = - 8$

Step 1

Move all terms to the left side of the equation and simplify.

Add $8$ to both sides of the equation.

$- 7 x^{2} + 7 x + 1 + 8 = 0$

Add $1$ and $8$ .

$- 7 x^{2} + 7 x + 9 = 0$

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 $a = - 7$ , $b = 7$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (- 7 \cdot 9)}}{2 \cdot - 7}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot - 7 \cdot 9}}{2 \cdot - 7}$

Multiply $- 4 \cdot - 7 \cdot 9$ .

Multiply $- 4$ by $- 7$ .

$x = \frac{- 7 \pm \sqrt{49 + 28 \cdot 9}}{2 \cdot - 7}$

Multiply $28$ by $9$ .

$x = \frac{- 7 \pm \sqrt{49 + 252}}{2 \cdot - 7}$

Add $49$ and $252$ .

$x = \frac{- 7 \pm \sqrt{301}}{2 \cdot - 7}$

Multiply $2$ by $- 7$ .

$x = \frac{- 7 \pm \sqrt{301}}{- 14}$

Simplify $\frac{- 7 \pm \sqrt{301}}{- 14}$ .

$x = \frac{7 \pm \sqrt{301}}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm \sqrt{301}}{14}$

Decimal Form:

$x = 1.73923939 \dots, - 0.73923939 \dots$