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 can substitute \( x = -3 \) into the equation and check if it holds true.

  1. Substitute \( x = -3 \) into the equation: \[ -3(-3)^2 - 9(-3) = 0 \]

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

  3. Multiply by -3: \[ -3 \cdot 9 = -27 \]

  4. Calculate \( -9 \cdot (-3) \): \[ -9 \cdot -3 = 27 \]

  5. Now combine these results: \[ -27 + 27 = 0 \]

Since the left side equals zero, we have confirmed that substituting \( x = -3 \) into the equation satisfies \( -3x^2 - 9x = 0 \).

Therefore, the conclusion is that \( x = -3 \) is indeed a solution to the quadratic equation \( -3x^2 - 9x = 0 \).