Solve the equation by the quadratic formula.
-$$2 x ^ { 2 } + 12 x + 3 = 0$$
A) $$\frac { - 12 \pm \sqrt { 30 } } { 2 }$$
B) $$\frac { - 6 \pm \sqrt { 30 } } { 4 }$$
C) $$\frac { - 6 \pm \sqrt { 42 } } { 2 }$$
D) $$\frac { - 6 \pm \sqrt { 30 } } { 2 }$$

Question

Quizplus · Accepted Answer

The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. For the equation $2x^2 + 12x + 3 = 0$, $a = 2$, $b = 12$, and $c = 3$. Plugging these into the formula gives $$x = \frac{-12 \pm \sqrt{12^2 - 4 \cdot 2 \cdot 3}}{4}$$, which simplifies to $$x = \frac{-12 \pm \sqrt{144 - 24}}{4}$$, or $$x = \frac{-12 \pm \sqrt{120}}{4}$$. Simplifying further, $\sqrt{120} = \sqrt{4 \cdot 30} = 2\sqrt{30}$, so $$x = \frac{-12 \pm 2\sqrt{30}}{4}$$, which simplifies to $$x = \frac{-6 \pm \sqrt{30}}{2}$$.

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

Solve the Equation by the Quadratic Formula $2 x ^ { 2 } + 12 x + 3 = 0$