Ariel is trying to determine if x = -3 is a solution to the quadratic equation -3x^2 - 9x = 0. Which explanation demonstrates the correct reasoning?

1 answer

To determine if \( x = -3 \) is a solution to the quadratic equation \(-3x^2 - 9x = 0\), we need to substitute \( x = -3 \) into the equation and see if it holds true.

Starting with the equation: \[ -3x^2 - 9x = 0 \]

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

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

Now simplifying: \[ -27 + 27 = 0 \]

This simplifies to: \[ 0 = 0 \]

Since this statement is true, it demonstrates that \( x = -3 \) is indeed a solution to the equation \(-3x^2 - 9x = 0\).

Therefore, the correct reasoning is that substituting \( -3 \) into the equation yields a true statement, confirming that \( x = -3 \) is a solution.