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)%0D%0AResponses%0D%0A%0D%0ANo, x=−3 is not a solution because substituting it back into the equation results in the following:%0D%0A%0D%0Ax%09Substituted%09Evaluate%09True Statement?%0D%0A−3%09−3(−3)2−9(−3)=0%09−54≠0%09FalseNo, 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%0D%0A%0D%0AYes, x=−3 is a solution because substituting it back into the equation results in the following:%0D%0A%0D%0Ax%09Substituted%09Evaluate%09True Statement?%0D%0A−3%09−3(−3)2−9(−3)=0%0954=0%09TrueYes, 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%0D%0A%0D%0ANo, x=−3 is not a solution because substituting it back into the equation results in the following:%0D%0A%0D%0Ax%09Substituted%09Evaluate%09True Statement?%0D%0A−3%09−3(−3)2−9(−3)=0%0954≠0%09FalseNo, 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%0D%0A%0D%0AYes, x=−3 is a solution because substituting it back into the equation results in the following:%0D%0A%0D%0Ax%09Substituted%09Evaluate%09True Statement?%0D%0A−3%09−3(−3)2−9(−3)=0%090=0%09TrueYes, 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%0D%0ASkip to navigation%0D%0A%0D%0Apage 20 of 20

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)%0D%0AResponses%0D%0A%0D%0ANo, x=−3 is not a solution because substituting it back into the equation results in the following:%0D%0A%0D%0Ax%09Substituted%09Evaluate%09True Statement?%0D%0A−3%09−3(−3)2−9(−3)=0%09−54≠0%09FalseNo, 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%0D%0A%0D%0AYes, x=−3 is a solution because substituting it back into the equation results in the following:%0D%0A%0D%0Ax%09Substituted%09Evaluate%09True Statement?%0D%0A−3%09−3(−3)2−9(−3)=0%0954=0%09TrueYes, 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%0D%0A%0D%0ANo, x=−3 is not a solution because substituting it back into the equation results in the following:%0D%0A%0D%0Ax%09Substituted%09Evaluate%09True Statement?%0D%0A−3%09−3(−3)2−9(−3)=0%0954≠0%09FalseNo, 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%0D%0A%0D%0AYes, x=−3 is a solution because substituting it back into the equation results in the following:%0D%0A%0D%0Ax%09Substituted%09Evaluate%09True Statement?%0D%0A−3%09−3(−3)2−9(−3)=0%090=0%09TrueYes, 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%0D%0ASkip to navigation%0D%0A%0D%0Apage 20 of 20

Answer 1

Ariel is trying to determine if \( x=-3 \) is a solution to the quadratic equation \( -3x^2-9x=0 \). To do this, Ariel can substitute \( x=-3 \) into the equation and see if it results in a true statement. Let's perform this substitution:

Original equation:
\( -3x^2-9x=0 \)

Substitute \( x=-3 \):
\( -3(-3)^2-9(-3)=0 \)

Now, evaluate the square and the multiplication:
\( -3(9)-(-27)=0 \)
\( -27+27=0 \)
\( 0=0 \)

This is a true statement. Therefore, the correct explanation is:

Yes, \( x=-3 \) is a solution because substituting it back into the equation results in a true statement:

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

So the last response provided is the correct reasoning showing that \( x=-3 \) is indeed a solution to the quadratic equation.