Solve the equation using the quadratic formula.
-$$4 x ^ { 2 } = - 12 x - 6$$
A) $x = \frac { - 3 + \sqrt { 3 } } { 2 }$ or $x = \frac { - 3 - \sqrt { 3 } } { 2 }$
B) $x = \frac { - 12 + \sqrt { 3 } } { 2 }$ or $x = \frac { - 12 - \sqrt { 3 } } { 2 }$
C) $x = \frac { - 3 + \sqrt { 15 } } { 2 }$ or $x = \frac { - 3 - \sqrt { 15 } } { 2 }$
D) $x = \frac { - 3 + \sqrt { 3 } } { 8 }$ or $x = \frac { - 3 - \sqrt { 3 } } { 8 }$

Question

Quizplus · Accepted Answer

The equation is in the form of $ax^2 + bx + c = 0$, where $a = 4$, $b = -12$, and $c = -6$. Using the quadratic formula, $x = \frac {-b \pm \sqrt {b^2 - 4ac}} {2a}$, we get:$x = \frac {-(-12) \pm \sqrt {(-12)^2 - 4(4)(-6)}} {2(4)}$$x = \frac {12 \pm \sqrt {144 + 96}} {8}$$x = \frac {12 \pm \sqrt {240}} {8}$$x = \frac {12 \pm \sqrt {16 \cdot 15}} {8}$$x = \frac {12 \pm 4\sqrt {15}} {8}$$x = \frac {3 \pm \sqrt {15}} {2}$Therefore, the correct answer is A.

Solve the Equation Using the Quadratic Formula 4x2=−12x−64 x ^ { 2 } = - 12 x - 64x2=−12x−6

Solve the Equation Using the Quadratic Formula $4 x ^ { 2 } = - 12 x - 6$