Solve.
-$$6 n ^ { 2 } = - 12 n - 1$$
A) $\frac { - 6 \pm \sqrt { 42 } } { 6 }$
B) $\frac { - 6 \pm \sqrt { 30 } } { 12 }$
C) $\frac { - 12 \pm \sqrt { 30 } } { 6 }$
D) $\frac { - 6 \pm \sqrt { 30 } } { 6 }$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $6n^2 = -12n - 1$, first bring all terms to one side to get $6n^2 + 12n + 1 = 0$. Then, use the quadratic formula $n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 6$, $b = 12$, and $c = 1$. Plugging these values in gives $n = \frac{-12 \pm \sqrt{(12)^2 - 4(6)(1)}}{2(6)} = \frac{-12 \pm \sqrt{144 - 24}}{12} = \frac{-12 \pm \sqrt{120}}{12} = \frac{-12 \pm \sqrt{30 \cdot 4}}{12} = \frac{-6 \pm \sqrt{30}}{6}$.

Solve - 6n2=−12n−16 n ^ { 2 } = - 12 n - 16n2=−12n−1

Solve
- $6 n ^ { 2 } = - 12 n - 1$