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

1 answer

To determine if x=3 is a solution to the equation 3x29x=0, we can substitute x=3 into the equation and simplify.

Let's check this step by step.

  1. Substitute x=3: 3(3)29(3)

  2. Calculate (3)2: (3)2=9 So, we have: 3(9)9(3)

  3. Compute: 27+27 This simplifies to: 0

Since substituting x=3 gives us 0, which is equal to the right side of the equation, this means x=3 is indeed a solution.

The correct answer is:

Yes, x=3 is a solution because substituting it back into the equation results in the following:

3(3)29(3)=0

0=0 (True)