Solve the equation using the quadratic formula.
-$$5 = - \frac { 12 } { x } - \frac { 1 } { x ^ { 2 } }$$
A) $\left\{ \frac { - 6 \pm \sqrt { 41 } } { 5 } \right\}$
B) $\left\{ \frac { - 6 \pm \sqrt { 31 } } { 10 } \right\}$
C) $\left\{ \frac { - 12 \pm \sqrt { 31 } } { 5 } \right\}$
D) $\left\{ \frac { - 6 \pm \sqrt { 31 } } { 5 } \right\}$

Question

Quizplus · Accepted Answer

Rewriting the equation as $x^2(5) = -12x - 1$ and rearranging gives $5x^2 + 12x + 1 = 0$. Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 5$, $b = 12$, $c = 1$, we find the solutions are $\frac{-12 \pm \sqrt{144 - 20}}{10} = \frac{-12 \pm \sqrt{124}}{10} = \frac{-6 \pm \sqrt{31}}{5}$.

Solve the Equation Using the Quadratic Formula 5=−12x−1x25 = - \frac { 12 } { x } - \frac { 1 } { x ^ { 2 } }5=−x12​−x21​

Solve the Equation Using the Quadratic Formula $5 = - \frac { 12 } { x } - \frac { 1 } { x ^ { 2 } }$