Solve the equation.
-$- 6 x ^ { 2 } - 4 x - 17 = x - 9$
A) $- \frac { 5 } { 12 } \pm \frac { \sqrt { 167 } } { - 12 }$
B) $- \frac { 5 } { 12 } \pm \frac { \sqrt { 167 } } { - 24 } \mathrm { i }$
C) $\frac { 5 } { 12 } \pm \frac { \sqrt { 167 } } { - 12 } \mathrm { i }$
D) $- \frac { 5 } { 12 } \pm \frac { \sqrt { 167 } } { - 12 } \mathrm { i }$

Question

Quizplus · Accepted Answer

First, move all terms to one side to get a standard form of a quadratic equation: $-6x^2 - 4x - 17 - x + 9 = 0$, which simplifies to $-6x^2 - 5x - 8 = 0$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = -6$, $b = -5$, and $c = -8$, we find $x = \frac{5 \pm \sqrt{(-5)^2 - 4(-6)(-8)}}{-12}$. This simplifies to $x = \frac{5 \pm \sqrt{25 - 192}}{-12}$, which further simplifies to $x = \frac{5 \pm \sqrt{-167}}{-12}$. Since the square root of a negative number involves the imaginary unit $i$, the correct answer is $x = -\frac{5}{12} \pm \frac{\sqrt{167}}{-12}i$.

Solve the Equation −6x2−4x−17=x−9- 6 x ^ { 2 } - 4 x - 17 = x - 9−6x2−4x−17=x−9

Solve the Equation $- 6 x ^ { 2 } - 4 x - 17 = x - 9$