Asked by T-Swizzle
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
Answered by
GPT-4o mini
To determine if \( x = -3 \) is a solution to the quadratic equation \(-3x^2 - 9x = 0\), we need to substitute \( x = -3 \) into the equation and see if it holds true.
Starting with the equation:
\[
-3x^2 - 9x = 0
\]
Substituting \( x = -3 \):
\[
-3(-3)^2 - 9(-3) = 0
\]
Calculating \((-3)^2\):
\[
-3(9) - 9(-3) = 0
\]
Now simplifying:
\[
-27 + 27 = 0
\]
This simplifies to:
\[
0 = 0
\]
Since this statement is true, it demonstrates that \( x = -3 \) is indeed a solution to the equation \(-3x^2 - 9x = 0\).
Therefore, the correct reasoning is that substituting \( -3 \) into the equation yields a true statement, confirming that \( x = -3 \) is a solution.
Starting with the equation:
\[
-3x^2 - 9x = 0
\]
Substituting \( x = -3 \):
\[
-3(-3)^2 - 9(-3) = 0
\]
Calculating \((-3)^2\):
\[
-3(9) - 9(-3) = 0
\]
Now simplifying:
\[
-27 + 27 = 0
\]
This simplifies to:
\[
0 = 0
\]
Since this statement is true, it demonstrates that \( x = -3 \) is indeed a solution to the equation \(-3x^2 - 9x = 0\).
Therefore, the correct reasoning is that substituting \( -3 \) into the equation yields a true statement, confirming that \( x = -3 \) is a solution.