Question

Using the quadratic formula, find the solution to 3x^2+18x+24=0
(1 point)
Responses

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

x = - 2
x = - 2

x = 4, x = 2
x = 4, x = 2

x= - 4

Answer 1

To solve the quadratic equation \(3x^2 + 18x + 24 = 0\) using the quadratic formula, we start by identifying the coefficients \(a\), \(b\), and \(c\):

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

The quadratic formula is given by:

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

Now, we 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, substitute the values into the quadratic formula:

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

Calculating the square root:

\[
\sqrt{36} = 6
\]

Substituting back into the formula:

\[
x = \frac{-18 \pm 6}{6}
\]

Now, we calculate the two possible values for \(x\):

1. For \(x = \frac{-18 + 6}{6}\):
\[
x = \frac{-12}{6} = -2
\]

2. For \(x = \frac{-18 - 6}{6}\):
\[
x = \frac{-24}{6} = -4
\]

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

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

Therefore, the correct response is:
**x = -2, x = -4**