Question

Use the quadratic formula to find the solution to 4x^2+4x−15=0
(1 point)
Responses

x=1.5, x=−2.5
x=1.5, x=−2.5

x=−1.5, x=−2.5
x=−1.5, x=−2.5

x=1.5
x is equal to 1 point 5

x=−2.5
x is equal to negative 2 point 5

Answer 1

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

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

The quadratic formula is given by:

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

Now, we substitute the values of \( a \), \( b \), and \( c \) into the formula:

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

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

2. Now apply the quadratic formula:

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

3. This gives us two solutions:

\[
x_1 = \frac{-4 + 16}{8} = \frac{12}{8} = 1.5
\]

\[
x_2 = \frac{-4 - 16}{8} = \frac{-20}{8} = -2.5
\]

Thus, the solutions are:

\[
x = 1.5, \quad x = -2.5
\]

The correct response is:

**x=1.5, x=−2.5**