Use the square root property to solve the quadratic equation.
-$3 x ^ { 2 } = - 6 x - 2$
A) $\frac { - 6 \pm \sqrt { 3 } } { 3 }$
B) $\frac { - 3 \pm \sqrt { 3 } } { 3 }$
C) $\frac { - 3 \pm \sqrt { 3 } } { 6 }$
D) $\frac { - 3 \pm \sqrt { 15 } } { 3 }$

Question

Quizplus · Accepted Answer

First, rearrange the equation to the form $ax^2 + bx + c = 0$, giving $3x^2 + 6x + 2 = 0$. Then, divide the entire equation by 3 to simplify, resulting in $x^2 + 2x + \frac{2}{3} = 0$. Completing the square or using the quadratic formula, where $a = 1$, $b = 2$, and $c = \frac{2}{3}$, leads to the solution $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, which simplifies to $x = \frac{-2 \pm \sqrt{4 - \frac{8}{3}}}{2}$ or $x = \frac{-2 \pm \sqrt{\frac{4}{3}}}{2}$, further simplifying to $x = \frac{-2 \pm 2\sqrt{\frac{1}{3}}}{2}$ or $x = \frac{-2 \pm \sqrt{3}}{2}$, which simplifies to $x = \frac{-1 \pm \sqrt{3}}{3}$, matching choice B.

Use the Square Root Property to Solve the Quadratic Equation 3x2=−6x−23 x ^ { 2 } = - 6 x - 23x2=−6x−2

Use the Square Root Property to Solve the Quadratic Equation $3 x ^ { 2 } = - 6 x - 2$