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=2
x equals 4 ,  x equals 2

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

x=−4

Answer 1

To solve the quadratic equation \(3x^2 + 18x + 24 = 0\) using the quadratic formula, we first identify the coefficients:

- \(a = 3\)
- \(b = 18\)
- \(c = 24\)

The quadratic formula is given by:

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

Now, let's calculate the discriminant, \(b^2 - 4ac\):

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

Now plug the values into the quadratic formula:

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

Calculating the two possible solutions:

1. First solution:
\[
x = \frac{{-18 + 6}}{6} = \frac{{-12}}{6} = -2
\]

2. Second solution:
\[
x = \frac{{-18 - 6}}{6} = \frac{{-24}}{6} = -4
\]

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

\[
x = -2, \quad x = -4
\]

From the provided response options, the correct answer is:

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