Question

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

x=−2.5
x equals negative 2.5

x=1.5, x=−2.5
x equals 1.5 , x equals negative 2.5

x=1.5
x equals 1.5

x=−1.5, x=−2.5

Answer 1

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

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

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

1. Calculate \(b^2 - 4ac\):
\[
b^2 = 4^2 = 16
\]
\[
4ac = 4 \cdot 4 \cdot (-15) = -240
\]
\[
b^2 - 4ac = 16 - (-240) = 16 + 240 = 256
\]

2. Calculate the square root:
\[
\sqrt{256} = 16
\]

3. Substitute back into the quadratic formula:
\[
x = \frac{-4 \pm 16}{2 \cdot 4}
\]
\[
x = \frac{-4 \pm 16}{8}
\]

4. Calculate the two possible values for \(x\):
- First solution:
\[
x = \frac{-4 + 16}{8} = \frac{12}{8} = \frac{3}{2} = 1.5
\]
- Second solution:
\[
x = \frac{-4 - 16}{8} = \frac{-20}{8} = -2.5
\]

Thus, the solutions are:
\[
x = 1.5 \quad \text{and} \quad x = -2.5
\]

So the correct answer is:
**x = 1.5, x = -2.5** (or "x equals 1.5, x equals negative 2.5").