Solve Using the Quadratic Formula 2x^2+12x=66

$2 x^{2} + 12 x = 66$

Step 1

Subtract $66$ from both sides of the equation.

$2 x^{2} + 12 x - 66 = 0$

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 $c = - 66$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (2 \cdot - 66)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 2 \cdot - 66}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 66$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 8 \cdot - 66}}{2 \cdot 2}$

Multiply $- 8$ by $- 66$ .

$x = \frac{- 12 \pm \sqrt{144 + 528}}{2 \cdot 2}$

Add $144$ and $528$ .

$x = \frac{- 12 \pm \sqrt{672}}{2 \cdot 2}$

Rewrite $672$ as $4^{2} \cdot 42$ .

Factor $16$ out of $672$ .

$x = \frac{- 12 \pm \sqrt{16 (42)}}{2 \cdot 2}$

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

$x = \frac{- 12 \pm \sqrt{4^{2} \cdot 42}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 4 \sqrt{42}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 12 \pm 4 \sqrt{42}}{4}$

Simplify $\frac{- 12 \pm 4 \sqrt{42}}{4}$ .

$x = - 3 \pm \sqrt{42}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 3 \pm \sqrt{42}$

Decimal Form:

$x = 3.48074069 \dots, - 9.48074069 \dots$