Solve the equation using the quadratic formula.
-$$6 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }$$
A) $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 6 } \right\}$
B) $\left\{ \frac { - 6 \pm \sqrt { 3 } } { 6 } \right\}$
C) $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 12 } \right\}$
D) $\left\{ \frac { - 3 \pm \sqrt { 15 } } { 6 } \right\}$

Question

Quizplus · Accepted Answer

First, multiply the entire equation by $x^2$ to get rid of the denominators, resulting in $6x^2 = -6x - 1$. Rearranging gives $6x^2 + 6x + 1 = 0$. Applying the quadratic formula, $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 6$, $b = 6$, and $c = 1$, yields solutions $\frac{-6 \pm \sqrt{36 - 24}}{12}$, which simplifies to $\frac{-6 \pm \sqrt{12}}{12}$ or $\frac{-6 \pm 2\sqrt{3}}{12}$, further simplifying to $\frac{-3 \pm \sqrt{3}}{6}$.

Solve the Equation Using the Quadratic Formula 6=−6x−1x26 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }6=−x6​−x21​

Solve the Equation Using the Quadratic Formula $6 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }$