Question

Ariel is trying to determine if x=−3 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 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

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 54=0 True

Answer 1

To determine whether \( x = -3 \) is a solution to the quadratic equation \( -3x^2 - 9x = 0 \), we need to substitute \( -3 \) into the equation and see if we end up with a true statement.

Substituting \( x = -3 \):

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

Calculating step by step:

1. Calculate \( (-3)^2 \):
\[
(-3)^2 = 9
\]

2. Substitute back into the equation:
\[
-3(9) - 9(-3)
\]

3. Calculate:
\[
-27 + 27 = 0
\]

Since this simplifies to \( 0 = 0 \), it 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:**

x Substituted Evaluate True Statement?
\(-3\) \(-3(-3)^2 - 9(-3) = 0\) \(0 = 0\) True

This indicates that the correct response is the one affirming that \( x = -3 \) is indeed a solution.