Solve the equation by completing the square. Express any complex numbers using i notation.
-$$3 x ^ { 2 } + 12 x + 3 = 2$$
A) $ x=\frac{-6 \pm \sqrt{39}}{3}$
B) $x = \frac { - 6 \pm \sqrt { 33 } } { 3 }$
C) $x = \frac { - 6 \pm \sqrt { 33 } } { 6 }$
D) $x = \frac { - 12 \pm \sqrt { 33 } } { 3 }$

Question

Quizplus · Accepted Answer

First, subtract 2 from both sides to get $3x^2 + 12x + 1 = 0$. Divide the entire equation by 3 to simplify: $x^2 + 4x + \frac{1}{3} = 0$. Complete the square by adding and subtracting $(\frac{4}{2})^2 = 4$ inside the equation: $x^2 + 4x + 4 = \frac{11}{3}$. This gives $(x + 2)^2 = \frac{11}{3}$. Solving for $x$ gives $x = -2 \pm \sqrt{\frac{11}{3}}$, which simplifies to $x = \frac{-6 \pm \sqrt{33}}{3}$.

Solve the Equation by Completing the Square 3x2+12x+3=23 x ^ { 2 } + 12 x + 3 = 23x2+12x+3=2

Solve the Equation by Completing the Square $3 x ^ { 2 } + 12 x + 3 = 2$