Question

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

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

x=−2
x equals negative 2

x=−4
x equals negative 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:

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

The quadratic formula is given by:

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

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

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

Now we substitute the values into the quadratic formula:

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

Now we have:

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

This gives us two solutions:

1. For the plus sign:

\[
x = \frac{{-18 + 6}}{6} = \frac{{-12}}{6} = -2
\]

2. For the minus sign:

\[
x = \frac{{-18 - 6}}{6} = \frac{{-24}}{6} = -4
\]

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

The correct option from your responses is:

**x=−2, x=−4**