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 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
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
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Answer 1

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

Let's break down the substitution:

1. Substitute \( x = -3 \):
\[
-3(-3)^2 - 9(-3)
\]

2. Evaluate:
- First, calculate \( (-3)^2 \):
\[
(-3)^2 = 9
\]
- Then substitute back:
\[
-3(9) - 9(-3)
\]
- This becomes:
\[
-27 + 27
\]
- Which simplifies to:
\[
0
\]

Since substituting \( x = -3 \) results in \( 0 = 0 \), we conclude that \( x = -3 \) is indeed a solution to the equation.

Thus, the correct response is:

**Yes, x = -3 is a solution because substituting it back into the equation results in the following:**
\[
-3(-3)^2 - 9(-3) = 0 \implies 0 = 0 \text{ (True)}
\]

This indicates that the first response is the correct reasoning.