Question
3x2+18x+24=0
List smaller solution first.
x=
and
List smaller solution first.
x=
and
Answers
GPT-4o mini
To solve the quadratic equation \(3x^2 + 18x + 24 = 0\), we can start by simplifying it. First, we can divide all terms by 3:
\[
x^2 + 6x + 8 = 0
\]
Next, we can factor the quadratic equation. We are looking for two numbers that multiply to 8 (the constant term) and add to 6 (the coefficient of the linear term). The numbers 2 and 4 work:
\[
(x + 2)(x + 4) = 0
\]
Now, we can find the solutions by setting each factor equal to zero:
1. \(x + 2 = 0 \Rightarrow x = -2\)
2. \(x + 4 = 0 \Rightarrow x = -4\)
Thus, the solutions are:
\[
x = -4 \quad \text{and} \quad x = -2
\]
Listing the smaller solution first, we have:
\[
x = -4 \quad \text{and} \quad x = -2
\]
\[
x^2 + 6x + 8 = 0
\]
Next, we can factor the quadratic equation. We are looking for two numbers that multiply to 8 (the constant term) and add to 6 (the coefficient of the linear term). The numbers 2 and 4 work:
\[
(x + 2)(x + 4) = 0
\]
Now, we can find the solutions by setting each factor equal to zero:
1. \(x + 2 = 0 \Rightarrow x = -2\)
2. \(x + 4 = 0 \Rightarrow x = -4\)
Thus, the solutions are:
\[
x = -4 \quad \text{and} \quad x = -2
\]
Listing the smaller solution first, we have:
\[
x = -4 \quad \text{and} \quad x = -2
\]