Question

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

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

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

x=−2.5
x equals negative 2.5

x=1.5

Answer 1

To solve the quadratic equation \(4x^2 + 4x - 15 = 0\) using the quadratic formula, we first identify the coefficients \(a\), \(b\), and \(c\) from the standard form of a quadratic equation, \(ax^2 + bx + c = 0\):

- \(a = 4\)
- \(b = 4\)
- \(c = -15\)

The quadratic formula is given by:

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

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

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

Next, we apply the quadratic formula:

\[
x = \frac{-4 \pm \sqrt{256}}{2 \cdot 4}
\]
\[
= \frac{-4 \pm 16}{8}
\]

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

1. For \(x = \frac{-4 + 16}{8}\):

\[
x = \frac{12}{8} = \frac{3}{2} = 1.5
\]

2. For \(x = \frac{-4 - 16}{8}\):

\[
x = \frac{-20}{8} = -\frac{5}{2} = -2.5
\]

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 equals 1.5, x equals negative 2.5.**