Question

Using the quadratic formula, find the solution to 3x2+18x+24=0 .(1 point)
Responses

x=−2
x equals negative 2

x=−4
x equals negative 4

x=−2, x=−4
x equals negative 2 , x equals negative 4

x=4, x=2

Answer 1

To solve the quadratic equation \(3x^2 + 18x + 24 = 0\) using the quadratic formula, we need the coefficients \(a\), \(b\), and \(c\) from the standard form \(ax^2 + bx + c = 0\).

Here, \(a = 3\), \(b = 18\), and \(c = 24\).

The quadratic formula is given by:

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

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

\[
b^2 = 18^2 = 324
\]
\[
4ac = 4 \cdot 3 \cdot 24 = 288
\]
\[
b^2 - 4ac = 324 - 288 = 36
\]

Now that we have the discriminant, we can substitute it back into the quadratic formula:

\[
x = \frac{-18 \pm \sqrt{36}}{2 \cdot 3}
\]
\[
x = \frac{-18 \pm 6}{6}
\]

Now we have two possible solutions:

1. For the positive case:
\[
x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2
\]

2. For the negative case:
\[
x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4
\]

Thus, the solutions to the equation \(3x^2 + 18x + 24 = 0\) are:

\[
x = -2 \quad \text{and} \quad x = -4
\]

Therefore, the correct response is:

**x = -2, x = -4**