Question

Use the quadratic formula to solve the equation.negative 4x squarednegative 11xplus3equals0Question content area bottomPart 1Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.A.xequalsenter your response here​(Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation \(-4x^2 - 11x + 3 = 0\) using the quadratic formula, we start with the standard form of the quadratic equation:

\[
ax^2 + bx + c = 0
\]

where
- \(a = -4\),
- \(b = -11\),
- \(c = 3\).

The quadratic formula is given by:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

1. Calculate the discriminant (\(b^2 - 4ac\)):
- \(b^2 = (-11)^2 = 121\)
- \(4ac = 4 \cdot (-4) \cdot 3 = -48\)

So,

\[
b^2 - 4ac = 121 - (-48) = 121 + 48 = 169
\]

2. Now plug the values into the quadratic formula:

\[
x = \frac{-(-11) \pm \sqrt{169}}{2(-4)} = \frac{11 \pm 13}{-8}
\]

3. This gives us two possible solutions:

- First solution:
\[
x = \frac{11 + 13}{-8} = \frac{24}{-8} = -3
\]

- Second solution:
\[
x = \frac{11 - 13}{-8} = \frac{-2}{-8} = \frac{1}{4}
\]

Thus, the solutions to the equation \(-4x^2 - 11x + 3 = 0\) are:

\[
x = -3, \frac{1}{4}
\]

**Final Answer:**

\(x = -3, \frac{1}{4}\)