Use the quadratic formula to solve the equation.negative 2x squarednegative 3xplus2equals0Question 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.)B.The solution is not a real number

Answer 1

To solve the quadratic equation \(-2x^2 - 3x + 2 = 0\) using the quadratic formula, we first identify the coefficients \(a\), \(b\), and \(c\) from the equation in the standard form \(ax^2 + bx + c = 0\):

• \(a = -2\)
• \(b = -3\)
• \(c = 2\)

The quadratic formula is given by:

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

Now, we will substitute the values of \(a\), \(b\), and \(c\) into the formula.

1. Calculate the discriminant (\(b^2 - 4ac\)):

\[ b^2 = (-3)^2 = 9 \]

\[ 4ac = 4 \cdot (-2) \cdot 2 = -16 \]

\[ b^2 - 4ac = 9 - (-16) = 9 + 16 = 25 \]

2. Now substitute into the quadratic formula:

\[ x = \frac{-(-3) \pm \sqrt{25}}{2 \cdot -2} \]

\[ x = \frac{3 \pm 5}{-4} \]

Now we will calculate the two possible values for \(x\):

• For \(x = \frac{3 + 5}{-4}\):

\[ x = \frac{8}{-4} = -2 \]

• For \(x = \frac{3 - 5}{-4}\):

\[ x = \frac{-2}{-4} = \frac{1}{2} \]

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

\[ x = -2, \frac{1}{2} \]

So, you can choose option A:

A. \(x = -2, \frac{1}{2}\)