Solve the equation using the quadratic formula.
-$$6 x ^ { 2 } + 12 x = - 2$$
A) $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 3 } \right\}$

B) $\left\{ \frac { - 12 \pm \sqrt { 6 } } { 3 } \right\}$

C) $\left\{ \frac { - 3 \pm \sqrt { 6 } } { 3 } \right\}$

D) $\left\{ \frac { - 3 \pm \sqrt { 6 } } { 12 } \right\}$

Question

Solve the equation using the quadratic formula.
-$$6 x ^ { 2 } + 12 x = - 2$$
A) $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 3 } \right\}$

B) $\left\{ \frac { - 12 \pm \sqrt { 6 } } { 3 } \right\}$

C) $\left\{ \frac { - 3 \pm \sqrt { 6 } } { 3 } \right\}$

D) $\left\{ \frac { - 3 \pm \sqrt { 6 } } { 12 } \right\}$

Quizplus · Accepted Answer

First, rewrite the equation in standard form: $6x^2 + 12x + 2 = 0$. Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 6$, $b = 12$, and $c = 2$, we find $x = \frac{-12 \pm \sqrt{(12)^2 - 4(6)(2)}}{2(6)} = \frac{-12 \pm \sqrt{144 - 48}}{12} = \frac{-12 \pm \sqrt{96}}{12} = \frac{-12 \pm 4\sqrt{6}}{12} = \frac{-3 \pm \sqrt{6}}{3}$.

Solve the Equation Using the Quadratic Formula 6x2+12x=−26 x ^ { 2 } + 12 x = - 26x2+12x=−2

Solve the Equation Using the Quadratic Formula $6 x ^ { 2 } + 12 x = - 2$