Question
Ariel is trying to determine if x= -3 is a solution to the quadratic equation -3x^2 -9x =0. Which explanation demonstrates the correct reasoning?
Answers
GPT-4o mini
To determine if \( x = -3 \) is a solution to the equation \( -3x^2 - 9x = 0 \), we can substitute \( x \) with \(-3\) and see if the equation holds true.
Starting with the left side of the equation, substitute \( x = -3 \):
\[
-3(-3)^2 - 9(-3) = 0
\]
Now, calculate each term:
1. Compute \((-3)^2\):
\[
(-3)^2 = 9
\]
2. Substitute into the equation:
\[
-3(9) - 9(-3)
\]
3. This simplifies to:
\[
-27 + 27 = 0
\]
Since the left side simplifies to \( 0 \), which is equal to the right side of the equation, we have:
\[
0 = 0
\]
Thus, \( x = -3 \) is indeed a solution to the equation \( -3x^2 - 9x = 0 \).
Therefore, the correct reasoning is that substituting \( x = -3 \) into the equation results in a true statement, meaning that \( x = -3 \) is a solution.
Starting with the left side of the equation, substitute \( x = -3 \):
\[
-3(-3)^2 - 9(-3) = 0
\]
Now, calculate each term:
1. Compute \((-3)^2\):
\[
(-3)^2 = 9
\]
2. Substitute into the equation:
\[
-3(9) - 9(-3)
\]
3. This simplifies to:
\[
-27 + 27 = 0
\]
Since the left side simplifies to \( 0 \), which is equal to the right side of the equation, we have:
\[
0 = 0
\]
Thus, \( x = -3 \) is indeed a solution to the equation \( -3x^2 - 9x = 0 \).
Therefore, the correct reasoning is that substituting \( x = -3 \) into the equation results in a true statement, meaning that \( x = -3 \) is a solution.