Solve Using the Quadratic Formula 9x^2+18x+8=0

$9 x^{2} + 18 x + 8 = 0$

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 $a = 9$ , $b = 18$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{- 18 \pm \sqrt{18^{2} - 4 \cdot (9 \cdot 8)}}{2 \cdot 9}$

Step 3

Simplify.

Simplify the numerator.

Raise $18$ to the power of $2$ .

$x = \frac{- 18 \pm \sqrt{324 - 4 \cdot 9 \cdot 8}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot 8$ .

Multiply $- 4$ by $9$ .

$x = \frac{- 18 \pm \sqrt{324 - 36 \cdot 8}}{2 \cdot 9}$

Multiply $- 36$ by $8$ .

$x = \frac{- 18 \pm \sqrt{324 - 288}}{2 \cdot 9}$

Subtract $288$ from $324$ .

$x = \frac{- 18 \pm \sqrt{36}}{2 \cdot 9}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 18 \pm \sqrt{6^{2}}}{2 \cdot 9}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 18 \pm 6}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{- 18 \pm 6}{18}$

Simplify $\frac{- 18 \pm 6}{18}$ .

$x = \frac{- 3 \pm 1}{3}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{2}{3}, - \frac{4}{3}$