Solve.
-$$7 x ^ { 2 } = - 9 x - 3$$
A) $- \frac { 9 } { 14 } \pm \frac { \sqrt { 3 } } { 14 }$
B) $\frac { 9 } { 14 } \pm \frac { \sqrt { 3 } } { 14 }$
C) $- \frac { 9 } { 14 } \pm \frac { \sqrt { 3 } } { 14 } \mathrm { i }$
D) $\frac { 9 } { 14 } \pm \frac { \sqrt { 3 } } { 14 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $7x^2 = -9x - 3$, first bring all terms to one side to get $7x^2 + 9x + 3 = 0$. Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 7$, $b = 9$, and $c = 3$, we find the discriminant $b^2 - 4ac = 81 - 84 = -3$, which is negative. This means the solutions will involve complex numbers. Solving further, we get $x = \frac{-9 \pm \sqrt{-3}}{14} = -\frac{9}{14} \pm \frac{\sqrt{3}}{14}i$, which matches choice C.

Solve - 7x2=−9x−37 x ^ { 2 } = - 9 x - 37x2=−9x−3

Solve
- $7 x ^ { 2 } = - 9 x - 3$