Solve the Quadratic Equation: -4x² + 96x - 576 = 0

Solve the following equation:

$-4x^2+96x-576=0$

To solve this quadratic equation $-4x^2 + 96x - 576 = 0$, we will apply the quadratic formula:

• The general form of a quadratic equation is $ax^2 + bx + c = 0$.
• For this equation, the coefficients are $a = -4$, $b = 96$, and $c = -576$.
• The quadratic formula states: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
• First, compute the discriminant: $b^2 - 4ac = 96^2 - 4(-4)(-576)$.
• Calculate $96^2 = 9216$ and $4(-4)(-576) = 9216$ as well.
• Thus, the discriminant is $9216 - 9216 = 0$.
• A discriminant of zero indicates that there is exactly one real solution (a repeated root).
• Now substitute into the quadratic formula: $x = \frac{-96 \pm \sqrt{0}}{2(-4)}$.
• This simplifies to $x = \frac{-96}{-8}$.
• Further simplification gives $x = 12$.

Therefore, the solution to the equation is $x = 12$, which corresponds to answer choice 2.