Question

Use the quadratic formula to solve. Express your answer in simplest form.
2, x, squared, minus, 3, x, minus, 15, equals, minus, 4, x
2x
2
−3x−15=
−4x

Answer 1

To solve the equation \(2x^2 - 3x - 15 = -4x\), we first rearrange the equation to one side:

1. Add \(4x\) to both sides:

\[
2x^2 - 3x + 4x - 15 = 0
\]

This simplifies to:

\[
2x^2 + x - 15 = 0
\]

Now, we can use the quadratic formula to solve for \(x\). The quadratic formula is given by:

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

In our equation \(2x^2 + x - 15 = 0\), the coefficients are:
- \(a = 2\)
- \(b = 1\)
- \(c = -15\)

Next, we calculate the discriminant \(b^2 - 4ac\):

\[
b^2 - 4ac = 1^2 - 4(2)(-15) = 1 + 120 = 121
\]

Now we apply the quadratic formula:

\[
x = \frac{-1 \pm \sqrt{121}}{2(2)}
\]
\[
x = \frac{-1 \pm 11}{4}
\]

Now, we find the two possible solutions:

1. Using the positive root:
\[
x = \frac{-1 + 11}{4} = \frac{10}{4} = \frac{5}{2}
\]

2. Using the negative root:
\[
x = \frac{-1 - 11}{4} = \frac{-12}{4} = -3
\]

Thus, the solutions to the equation \(2x^2 + x - 15 = 0\) are:

\[
\boxed{\frac{5}{2}} \quad \text{and} \quad \boxed{-3}
\]