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 equals 1.5

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

x=1.5
, x=−2.5

Answer 1

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

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

In this case, the coefficients are:
- \(a = 4\)
- \(b = 4\)
- \(c = -15\)

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

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

Now, we plug the values into the quadratic formula:

\[
x = \frac{{-4 \pm \sqrt{256}}}{2 \cdot 4}
\]

Calculating \(\sqrt{256}\):

\[
\sqrt{256} = 16
\]

Now substitute back into the quadratic formula:

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

This gives us two solutions:

1. For the plus sign:
\[
x = \frac{{-4 + 16}}{8} = \frac{12}{8} = \frac{3}{2} = 1.5
\]

2. For the minus sign:
\[
x = \frac{{-4 - 16}}{8} = \frac{-20}{8} = -\frac{5}{2} = -2.5
\]

Thus, the solutions to the equation \(4x^2 + 4x - 15 = 0\) are:
\[
x = 1.5 \quad \text{and} \quad x = -2.5
\]

The correct response is:
**x = 1.5, x = -2.5**