Question

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

x=−2
x equals negative 2

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

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

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

Now we substitute the values of \(a\), \(b\), and \(c\) into the formula.

1. Calculate the discriminant (\(b^2 - 4ac\)):

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

2. Now substitute \(b\) and the discriminant into the quadratic formula:

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

3. Now we find the two possible values for \(x\):

- First, using the plus sign:
\[
x = \frac{{-18 + 6}}{6} = \frac{{-12}}{6} = -2
\]

- Second, using the minus sign:
\[
x = \frac{{-18 - 6}}{6} = \frac{{-24}}{6} = -4
\]

Thus, the solutions are:

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

Therefore, the correct response is:

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