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