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 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 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

Answer 1

To determine whether \( x = -3 \) is a solution to the equation \( -3x^2 - 9x = 0 \), we will substitute \( -3 \) for \( x \) and evaluate the equation.

Let's perform the substitution:

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

2. Calculate \( (-3)^2 \): \[ (-3)^2 = 9 \]

3. Now substitute that back into the equation: \[ -3(9) - 9(-3) \]

4. Simplify \( -3(9) \) and \( -9(-3) \): \[ -27 + 27 = 0 \]

So, substituting \( x = -3 \) into the equation results in: \[ 0 = 0 \]

This is a true statement. Thus, \( x = -3 \) is indeed a solution to the equation \( -3x^2 - 9x = 0 \).

The correct explanation demonstrating this 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, which simplifies to 0=0. True."