Quadratic Equations Online Practice

Question

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

x=1.5
x equals 1.5

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

x=−2.5
x equals negative 2.5

x=1.5
, x=−2.5
x equals 1.5 , x equals negative 2.5
Remaining Attempts : 3
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Answer 1

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

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

In the given equation, the coefficients are:

• \(a = 4\)
• \(b = 4\)
• \(c = -15\)

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

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

Now, we plug in the values into the quadratic formula:

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

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

Now we calculate the two possible solutions:

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

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

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

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

Thus, the solutions to the equation \(4x^2 + 4x - 15 = 0\) are:

\[ x = 1.5 \quad \text{and} \quad x = -2.5 \]

So the correct response would be:

x=1.5, x=−2.5