Solve Using the Quadratic Formula 8x^2-4x-18=0

$8 x^{2} - 4 x - 18 = 0$

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 $a = 8$ , $b = - 4$ , and $c = - 18$ into the quadratic formula and solve for $x$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (8 \cdot - 18)}}{2 \cdot 8}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 4$ to the power of $2$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 8 \cdot - 18}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot - 18$ .

Multiply $- 4$ by $8$ .

$x = \frac{4 \pm \sqrt{16 - 32 \cdot - 18}}{2 \cdot 8}$

Multiply $- 32$ by $- 18$ .

$x = \frac{4 \pm \sqrt{16 + 576}}{2 \cdot 8}$

Add $16$ and $576$ .

$x = \frac{4 \pm \sqrt{592}}{2 \cdot 8}$

Rewrite $592$ as $4^{2} \cdot 37$ .

Factor $16$ out of $592$ .

$x = \frac{4 \pm \sqrt{16 (37)}}{2 \cdot 8}$

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

$x = \frac{4 \pm \sqrt{4^{2} \cdot 37}}{2 \cdot 8}$

Pull terms out from under the radical.

$x = \frac{4 \pm 4 \sqrt{37}}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{4 \pm 4 \sqrt{37}}{16}$

Simplify $\frac{4 \pm 4 \sqrt{37}}{16}$ .

$x = \frac{1 \pm \sqrt{37}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{37}}{4}$

Decimal Form:

$x = 1.77069063 \dots, - 1.27069063 \dots$