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 see if it holds true.
The original equation is:
\[ -3x^2 - 9x = 0 \]
Substituting \( x = -3 \):
\[ -3(-3)^2 - 9(-3) = 0 \]
Calculating \( (-3)^2 \):
\[ = -3(9) + 27 \]
Now simplify:
\[ = -27 + 27 \]
\[ = 0 \]
Since the left-hand side evaluates to 0, we have:
\[ 0 = 0 \]
Thus, \( x = -3 \) is indeed a solution to the quadratic equation \( -3x^2 - 9x = 0 \).