Ariel is trying to determine if x=−3

Question

is a solution to the quadratic equation −3x2−9x=0
. Which explanation demonstrates the correct reasoning?(1 point)
Responses

No, x=−3
is not a solution because substituting it back into the equation results in the following:

x Substituted Evaluate True Statement?
−3
−3(−3)2−9(−3)=0
−54≠0
False
No, x equals negative 3 is not a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 negative 54 does not equal 0 False

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

x Substituted Evaluate True Statement?
−3
−3(−3)2−9(−3)=0
54=0
True
Yes, x equals negative 3 is a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 54 equals 0 True

No, x=−3
is not a solution because substituting it back into the equation results in the following:

x Substituted Evaluate True Statement?
−3
−3(−3)2−9(−3)=0
54≠0
False
No, x equals negative 3 is not a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 54 does not equal 0 False

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

x Substituted Evaluate True Statement?
−3
−3(−3)2−9(−3)=0
0=0
True
Yes, x equals negative 3 is a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 0 equals 0 True

Answer 1

To determine if \( x = -3 \) is a solution to the equation \( -3x^2 - 9x = 0 \), we can substitute \( -3 \) into the equation and simplify.

Substituting \( x = -3 \):

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

Calculating this step-by-step:

1. Calculate \( (-3)^2 = 9 \)
2. Substitute into the equation: \[ -3(9) - 9(-3) \]
3. Simplify: \[ -27 + 27 = 0 \]

Since the left side simplifies to \( 0 \), which matches the right side of the equation, \( 0 = 0 \) is a true statement.

Therefore, the correct reasoning is:

Yes, \( x = -3 \) is a solution because substituting it back into the equation results in the following:

\[ -3(-3)^2 - 9(-3) = 0 \quad \Rightarrow \quad 0 = 0 \quad \text{(True)} \]

So, the correct response is the one that states that \( x = -3 \) is indeed a solution, confirming that both sides of the equation equal \( 0 \).