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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
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

1 answer

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

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

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

  3. Calculate \( -3(9) \) and \( -9(-3) \): \[ -27 + 27 \]

  4. Combine the results: \[ -27 + 27 = 0 \]

Since the left-hand side equals 0, we can conclude that substituting \( x = -3 \) into the equation does indeed satisfy the equation.

Therefore, the correct explanation is:

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

  • Substituted: \(-3\)
  • Evaluate: \(-3(-3)^2 - 9(-3) = 0\)
  • True Statement? \(0 = 0\)
  • True

This indicates that \( x = -3 \) is indeed a solution of the quadratic equation.