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?

Question

A) Yes, x = −3 is a solution because substituting it back into the equation results in the following:
B) Yes, x = −3 is a solution because substituting it back into the equation results in the following:
C) No, x = −3 is not a solution because substituting it back into the equation results in the following:
D) No, x = −3 is not a solution because substituting it back into the equation results in the following:

Answer 1

To determine if \( x = -3 \) is a solution to the equation \( -3x^2 - 9x = 0 \), we should substitute \( -3 \) into the equation and verify whether the equation holds true.

Let's substitute \( x = -3 \):

\[ -3(-3)^2 - 9(-3) = 0 \]

Calculating \( (-3)^2 \):

\[ -3(9) + 27 = 0 \]

Now, calculating further:

\[ -27 + 27 = 0 \]

This simplifies to:

\[ 0 = 0 \]

Since the original equation holds true after substitution, we can conclude that \( x = -3 \) is indeed a solution.

Therefore, the correct explanation demonstrating the reasoning is:

A) Yes, x = −3 is a solution because substituting it back into the equation results in the following: 0 = 0.