Solve the equation by completing the square.
-$$2 x ^ { 2 } + 12 x + 3 = 0$$
A) $\left\{ \frac { - 12 - \sqrt { 30 } } { 2 } , \frac { - 12 + \sqrt { 30 } } { 2 } \right\}$
B) $\left\{ \frac { - 6 - \sqrt { 30 } } { 2 } , \frac { - 6 + \sqrt { 30 } } { 2 } \right\}$
C) $\left\{ \frac { - 6 - \sqrt { 30 } } { 4 } , \frac { - 6 + \sqrt { 30 } } { 4 } \right\}$
D) $\left\{ \frac { - 6 - \sqrt { 42 } } { 2 } , \frac { - 6 + \sqrt { 42 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $2x^2 + 12x + 3 = 0$ by completing the square, first divide the entire equation by 2 to simplify: $x^2 + 6x + \frac{3}{2} = 0$. Then, move the constant term to the other side: $x^2 + 6x = -\frac{3}{2}$. To complete the square, add $(\frac{6}{2})^2 = 9$ to both sides, resulting in $x^2 + 6x + 9 = \frac{15}{2}$. This gives $(x + 3)^2 = \frac{15}{2}$, and taking the square root of both sides yields $x + 3 = \pm \sqrt{\frac{15}{2}}$. Solving for $x$ gives $x = -3 \pm \sqrt{\frac{15}{2}}$, which simplifies to $x = -3 \pm \frac{\sqrt{30}}{2}$, or $\left\{ \frac{-6 - \sqrt{30}}{2}, \frac{-6 + \sqrt{30}}{2} \right\}$.

Solve the Equation by Completing the Square 2x2+12x+3=02 x ^ { 2 } + 12 x + 3 = 02x2+12x+3=0

Solve the Equation by Completing the Square $2 x ^ { 2 } + 12 x + 3 = 0$