Solve Using the Quadratic Formula 7x^2-16x=8

$7 x^{2} - 16 x = 8$

Step 1

Subtract $8$ from both sides of the equation.

$7 x^{2} - 16 x - 8 = 0$

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 $a = 7$ , $b = - 16$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (7 \cdot - 8)}}{2 \cdot 7}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 16$ to the power of $2$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 7 \cdot - 8}}{2 \cdot 7}$

Multiply $- 4 \cdot 7 \cdot - 8$ .

Multiply $- 4$ by $7$ .

$x = \frac{16 \pm \sqrt{256 - 28 \cdot - 8}}{2 \cdot 7}$

Multiply $- 28$ by $- 8$ .

$x = \frac{16 \pm \sqrt{256 + 224}}{2 \cdot 7}$

Add $256$ and $224$ .

$x = \frac{16 \pm \sqrt{480}}{2 \cdot 7}$

Rewrite $480$ as $4^{2} \cdot 30$ .

Factor $16$ out of $480$ .

$x = \frac{16 \pm \sqrt{16 (30)}}{2 \cdot 7}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{16 \pm \sqrt{4^{2} \cdot 30}}{2 \cdot 7}$

Pull terms out from under the radical.

$x = \frac{16 \pm 4 \sqrt{30}}{2 \cdot 7}$

Multiply $2$ by $7$ .

$x = \frac{16 \pm 4 \sqrt{30}}{14}$

Simplify $\frac{16 \pm 4 \sqrt{30}}{14}$ .

$x = \frac{8 \pm 2 \sqrt{30}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8 \pm 2 \sqrt{30}}{7}$

Decimal Form:

$x = 2.70777873 \dots, - 0.42206445 \dots$