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
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

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. Substituting $ x = -3 $: $$ -3(-3)^2 - 9(-3) = 0 $$ Calculating the first term: $$ -3(-3)^2 = -3(9) = -27 $$ Calculating the second term: $$ -9(-3) = 27 $$ Now, putting these together: $$ -27 + 27 = 0 $$ This simplifies to: $$ 0 = 0 $$ Since this statement is true, $ x = -3 $ is indeed a solution to the equation. The correct explanation demonstrating this reasoning is: **Yes, $ x = -3 $ is a solution because substituting it back into the equation results in the following:** $$ -3(-3)^2 - 9(-3) = 0 \implies 0 = 0 \text{ True} $$ Thus, the response confirming that $ x = -3 $ is a solution is accurate.