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=−4
x equals negative 4

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

x=−2

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, calculate the discriminant:

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

Next, since the discriminant is positive, we will have two real solutions. Now plug the values into the quadratic formula:

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

Calculate the two solutions:

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

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

So the solutions are:

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

Thus, the response is:

**x=−2, x=−4** (or **x equals negative 2 , x equals negative 4**)