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

Answer 1

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

Let's check this step by step.

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

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:**

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

\( 0 = 0 \) (True)