Solve Using the Quadratic Formula 9m^2+2m=8

$9 m^{2} + 2 m = 8$

Step 1

Subtract $8$ from both sides of the equation.

$9 m^{2} + 2 m - 8 = 0$

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 $a = 9$ , $b = 2$ , and $c = - 8$ into the quadratic formula and solve for $m$ .

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

Step 4

Simplify.

Simplify the numerator.

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

$m = \frac{- 2 \pm \sqrt{4 - 4 \cdot 9 \cdot - 8}}{2 \cdot 9}$

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

Multiply $- 4$ by $9$ .

$m = \frac{- 2 \pm \sqrt{4 - 36 \cdot - 8}}{2 \cdot 9}$

Multiply $- 36$ by $- 8$ .

$m = \frac{- 2 \pm \sqrt{4 + 288}}{2 \cdot 9}$

Add $4$ and $288$ .

$m = \frac{- 2 \pm \sqrt{292}}{2 \cdot 9}$

Rewrite $292$ as $2^{2} \cdot 73$ .

Factor $4$ out of $292$ .

$m = \frac{- 2 \pm \sqrt{4 (73)}}{2 \cdot 9}$

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

$m = \frac{- 2 \pm \sqrt{2^{2} \cdot 73}}{2 \cdot 9}$

Pull terms out from under the radical.

$m = \frac{- 2 \pm 2 \sqrt{73}}{2 \cdot 9}$

Multiply $2$ by $9$ .

$m = \frac{- 2 \pm 2 \sqrt{73}}{18}$

Simplify $\frac{- 2 \pm 2 \sqrt{73}}{18}$ .

$m = \frac{- 1 \pm \sqrt{73}}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = \frac{- 1 \pm \sqrt{73}}{9}$

Decimal Form:

$m = 0.83822263 \dots, - 1.06044486 \dots$