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Solution Sets of Quadratic Equations Quick Check

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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 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

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 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

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 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 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 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
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1 answer

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

Starting with the equation:

\[ -3x^2 - 9x = 0 \]

Substituting \( x = -3 \):

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

Calculating:

  1. Compute \( (-3)^2 = 9 \).
  2. Substitute this value into the equation:

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

  1. Simplify:

\[ -27 + 27 = 0 \]

This simplifies to:

\[ 0 = 0 \]

Since both sides of the equation are equal, \( x = -3 \) is indeed a solution.

The correct response is:

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

\[ -3(-3)^2 - 9(-3) = 0 \Rightarrow 0 = 0 \text{ (True)} \]