Solve Using the Quadratic Formula 2x^2+12x=10

$2 x^{2} + 12 x = 10$

Step 1

Subtract $10$ from both sides of the equation.

$2 x^{2} + 12 x - 10 = 0$

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 $a = 2$ , $b = 12$ , and $c = - 10$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (2 \cdot - 10)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 2 \cdot - 10}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 10$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 8 \cdot - 10}}{2 \cdot 2}$

Multiply $- 8$ by $- 10$ .

$x = \frac{- 12 \pm \sqrt{144 + 80}}{2 \cdot 2}$

Add $144$ and $80$ .

$x = \frac{- 12 \pm \sqrt{224}}{2 \cdot 2}$

Rewrite $224$ as $4^{2} \cdot 14$ .

Factor $16$ out of $224$ .

$x = \frac{- 12 \pm \sqrt{16 (14)}}{2 \cdot 2}$

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

$x = \frac{- 12 \pm \sqrt{4^{2} \cdot 14}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 4 \sqrt{14}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 12 \pm 4 \sqrt{14}}{4}$

Simplify $\frac{- 12 \pm 4 \sqrt{14}}{4}$ .

$x = - 3 \pm \sqrt{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 3 \pm \sqrt{14}$

Decimal Form:

$x = 0.74165738 \dots, - 6.74165738 \dots$