Solve Using the Quadratic Formula 6m^2+10m+2=0

$6 m^{2} + 10 m + 2 = 0$

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 $a = 6$ , $b = 10$ , and $c = 2$ into the quadratic formula and solve for $m$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (6 \cdot 2)}}{2 \cdot 6}$

Step 3

Simplify.

Simplify the numerator.

Raise $10$ to the power of $2$ .

$m = \frac{- 10 \pm \sqrt{100 - 4 \cdot 6 \cdot 2}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot 2$ .

Multiply $- 4$ by $6$ .

$m = \frac{- 10 \pm \sqrt{100 - 24 \cdot 2}}{2 \cdot 6}$

Multiply $- 24$ by $2$ .

$m = \frac{- 10 \pm \sqrt{100 - 48}}{2 \cdot 6}$

Subtract $48$ from $100$ .

$m = \frac{- 10 \pm \sqrt{52}}{2 \cdot 6}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$m = \frac{- 10 \pm \sqrt{4 (13)}}{2 \cdot 6}$

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

$m = \frac{- 10 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot 6}$

Pull terms out from under the radical.

$m = \frac{- 10 \pm 2 \sqrt{13}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$m = \frac{- 10 \pm 2 \sqrt{13}}{12}$

Simplify $\frac{- 10 \pm 2 \sqrt{13}}{12}$ .

$m = \frac{- 5 \pm \sqrt{13}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = \frac{- 5 \pm \sqrt{13}}{6}$

Decimal Form:

$m = - 0.23240812 \dots, - 1.43425854 \dots$