Question

Using the quadratic formula, find the solution to 3x2+18x+24=0 .(1 point) Responses x=−4 x equals negative 4 x=−2 x equals negative 2 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 first need to identify 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 let's calculate the discriminant \(b^2 - 4ac\):

\[
b^2 = 18^2 = 324
\]

\[
4ac = 4 \cdot 3 \cdot 24 = 288
\]

Now, calculate the discriminant:

\[
b^2 - 4ac = 324 - 288 = 36
\]

Now, plug the values into the quadratic formula:

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

Simplifying further:

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

This gives us two possible solutions:

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

2. \(x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4\)

Thus, the solutions are \(x = -2\) and \(x = -4\).

The correct response is:

**x = -2, x = -4** (or \(x\) equals negative 2, \(x\) equals negative 4).