Question
Using the factoring method, solve for the roots of the quadratic equation. Be sure to place your equation in standard form before factoring.3 x squared minus x equals negative 7 xQuestion content area bottomPart 1xequalsenter your response here (Simplify your answer. Use a comma to separate answers as needed.)
Answers
GPT-4o mini
To solve the quadratic equation using the factoring method, we first need to write the equation in standard form, which is \( ax^2 + bx + c = 0 \).
Given the equation:
\[ 3x^2 - x = -7x \]
We start by moving all terms to one side of the equation:
\[ 3x^2 - x + 7x = 0 \]
Combining like terms gives us:
\[ 3x^2 + 6x = 0 \]
Now, we can factor out the greatest common factor (GCF):
\[ 3x(x + 2) = 0 \]
Now, we can set each factor equal to zero:
1. \( 3x = 0 \)
2. \( x + 2 = 0 \)
Solving these equations:
1. From \( 3x = 0 \):
\[
x = 0
\]
2. From \( x + 2 = 0 \):
\[
x = -2
\]
Therefore, the roots of the quadratic equation are:
\[
x = 0, -2
\]
So the final answer is:
\[
\boxed{0, -2}
\]
Given the equation:
\[ 3x^2 - x = -7x \]
We start by moving all terms to one side of the equation:
\[ 3x^2 - x + 7x = 0 \]
Combining like terms gives us:
\[ 3x^2 + 6x = 0 \]
Now, we can factor out the greatest common factor (GCF):
\[ 3x(x + 2) = 0 \]
Now, we can set each factor equal to zero:
1. \( 3x = 0 \)
2. \( x + 2 = 0 \)
Solving these equations:
1. From \( 3x = 0 \):
\[
x = 0
\]
2. From \( x + 2 = 0 \):
\[
x = -2
\]
Therefore, the roots of the quadratic equation are:
\[
x = 0, -2
\]
So the final answer is:
\[
\boxed{0, -2}
\]