Question

Using the quadratic formula, find the solution to 4x2+4x−15=0.(1 point)
Responses

x=−2.5
x is equal to negative 2 point 5 - no response given

x=1.5
x is equal to 1 point 5 - incorrect

x=−1.5, x=−2.5
x is equal to negative 1 point 5, x is equal to negative 2 point 5 - no response given

x=1.5, x=−2.5

Answer 1

To solve the quadratic equation \(4x^2 + 4x - 15 = 0\) using the quadratic formula, we use:

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

Here, \(a = 4\), \(b = 4\), and \(c = -15\).

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

\[
b^2 - 4ac = 4^2 - 4(4)(-15) = 16 + 240 = 256
\]

2. **Calculate the square root of the discriminant**:

\[
\sqrt{256} = 16
\]

3. **Substitute \(b\), the square root of the discriminant, and \(a\) into the quadratic formula**:

\[
x = \frac{-4 \pm 16}{2(4)} = \frac{-4 \pm 16}{8}
\]

4. **Calculate the two possible values for \(x\)**:

- For the positive case (\(+\)):
\[
x = \frac{-4 + 16}{8} = \frac{12}{8} = 1.5
\]

- For the negative case (\(-\)):
\[
x = \frac{-4 - 16}{8} = \frac{-20}{8} = -2.5
\]

Thus, the solutions are:

\[
x = 1.5 \quad \text{and} \quad x = -2.5
\]

Therefore, the correct response is:

**x=1.5, x=−2.5**.