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	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

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

GPT-4o mini · Answer

To determine if $ x = -3 $ is a solution to the quadratic equation $ -3x^2 - 9x = 0 $, we substitute $ -3 $ into the equation and simplify. Substituting $ x = -3 $ gives: $$ -3(-3)^2 - 9(-3) = 0 $$ Calculating $ (-3)^2 $: $$ (-3)^2 = 9 $$ Now substituting into the equation: $$ -3(9) + 27 = 0 $$ $$ -27 + 27 = 0 $$ $$ 0 = 0 $$ The statement holds true. Thus, the correct explanation is: **Yes, $ x = -3 $ is a solution because substituting it back into the equation results in the following:** $$ -3(-3)^2 - 9(-3) = 0 \rightarrow 0 = 0 \text{ (True)} $$ This explanation correctly shows that $ x = -3 $ satisfies the equation, therefore it is indeed a solution.