Question

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?

Answer 1

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 \( -3x^2 - 9x = 0 \)**.