Ariel is trying to determine if x=−3 is a solution to the quadratic equation −3xexponent2 −9x=0 . Which explanation demonstrates the correct reasoning?(1 point)

Question

Responses

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)exponent2 −9(−3)=0 54≠0 FalseNo, 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)exponent2 −9(−3)=0 −54≠0 FalseNo, 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

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)exponent2 −9(−3)=0 0=0 TrueYes, 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

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)exponent2 −9(−3)=0 54=0 True

Answer 1

To determine if \( x = -3 \) is a solution to the quadratic equation \( -3x^2 - 9x = 0 \), let's substitute \( x = -3 \) into the equation:

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

First, calculate \( (-3)^2 \):

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

Now substitute this back into the equation:

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

Calculating \( -3(9) \):

\[ -27 \]

Calculating \( -9(-3) \):

\[ 27 \]

Now combine these results:

\[ -27 + 27 = 0 \]

So, the equation simplifies to:

\[ 0 = 0 \]

This is a true statement.

Therefore, the correct explanation that demonstrates the reasoning is:

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

This confirms that yes, \( x = -3 \) is a solution.

Answer 2

is it the first second third or forth?

Answer 3

The correct choice is the third response:

"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"

This clearly indicates that substituting \( x = -3 \) into the equation results in a true statement.