Question

Using the quadratic formula, find the solution to 3x2+18x+24=0
3
𝑥
2
+
18
𝑥
+
24
=
0
(1 point)
Responses

x=4
𝑥
=
4
x is equal to 4

x=−2
𝑥
=
−
2
x is equal to negative 2

x=4, x=2
𝑥
=
4
,

𝑥
=
2
x=4, x=2
𝑥
=
4
,

𝑥
=
2

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 in the standard form of a quadratic equation \( ax^2 + bx + c = 0 \).

Here, we have:
- \( a = 3 \)
- \( b = 18 \)
- \( c = 24 \)

The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Now we can substitute the values of \( a \), \( b \), and \( c \):

1. Calculate the discriminant \( b^2 - 4ac \):
\[
b^2 = 18^2 = 324
\]
\[
4ac = 4 \times 3 \times 24 = 288
\]
\[
b^2 - 4ac = 324 - 288 = 36
\]

2. Now substitute into the quadratic formula:
\[
x = \frac{-18 \pm \sqrt{36}}{2 \times 3}
\]
\[
\sqrt{36} = 6
\]
\[
x = \frac{-18 \pm 6}{6}
\]

3. This gives us two solutions:
- First solution:
\[
x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2
\]
- Second solution:
\[
x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4
\]

Thus, the solutions to the equation \( 3x^2 + 18x + 24 = 0 \) are:
\[
x = -2 \quad \text{and} \quad x = -4
\]

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