Ariel is trying to determine if x=−3

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

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

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

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

GPT-4o mini · Answer

To determine if $ x = -3 $ is a solution to the quadratic equation $ -3x^2 - 9x = 0 $, we need to substitute $ -3 $ into the equation and evaluate. Substituting $ x = -3 $ into the equation: $$ -3(-3)^2 - 9(-3) = 0 $$ Calculating each term: 1. $ (-3)^2 = 9 $ so $ -3(9) = -27 $ 2. $ -9(-3) = 27 $ Now combine these results: $$ -27 + 27 = 0 $$ This simplifies to: $$ 0 = 0 $$ Since this statement is true, $ x = -3 $ is indeed a solution to the equation. Therefore, the correct explanations are: **Yes, x = -3 is a solution because substituting it back into the equation results in the following:** -3(-3)^2 - 9(-3) = 0 0 = 0 True This corresponds to the responses that state $ 0 = 0 $ upon substitution, confirming it as a valid solution.