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

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

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

Answer 1

To determine if \( x = -3 \) is a solution to the quadratic equation \( -3x^2 - 9x = 0 \), we need to substitute \( -3 \) into the equation and evaluate.

Substituting \( x = -3 \) into the equation:

\[
-3(-3)^2 - 9(-3) = 0
\]

Calculating each term:

1. \( (-3)^2 = 9 \) so \( -3(9) = -27 \)
2. \( -9(-3) = 27 \)

Now combine these results:

\[
-27 + 27 = 0
\]

This simplifies to:

\[
0 = 0
\]

Since this statement is true, \( x = -3 \) is indeed a solution to the equation.

Therefore, the correct explanations are:

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

-3(-3)^2 - 9(-3) = 0
0 = 0
True

This corresponds to the responses that state \( 0 = 0 \) upon substitution, confirming it as a valid solution.