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)

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	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
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 negative 54 does not equal 0 False
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GPT-4o mini · Accepted Answer

To determine if $ x = -3 $ is a solution to the quadratic equation $ -3x^2 - 9x = 0 $, we can substitute $ -3 $ into the equation and evaluate it. Let's break down the substitution: 1. Substitute $ x = -3 $: $$ -3(-3)^2 - 9(-3) $$ 2. Evaluate: - First, calculate $ (-3)^2 $: $$ (-3)^2 = 9 $$ - Then substitute back: $$ -3(9) - 9(-3) $$ - This becomes: $$ -27 + 27 $$ - Which simplifies to: $$ 0 $$ Since substituting $ x = -3 $ results in $ 0 = 0 $, we conclude that $ x = -3 $ is indeed a solution to the equation. Thus, the correct response is: **Yes, x = -3 is a solution because substituting it back into the equation results in the following:** $$ -3(-3)^2 - 9(-3) = 0 \implies 0 = 0 \text{ (True)} $$ This indicates that the first response is the correct reasoning.