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.
Let's substitute \( x = -3 \):
\[ -3(-3)^2 - 9(-3) = 0 \]
Calculating each term:
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Calculate \((-3)^2\): \[ (-3)^2 = 9 \]
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Now substitute this back into the equation: \[ -3(9) - 9(-3) \]
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Compute \( -3(9) \): \[ -27 \]
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Compute \( -9(-3) \): \[ 27 \]
Now, combine these results:
\[ -27 + 27 = 0 \]
Since the left side of the equation equals to 0, we have:
\[ 0 = 0 \]
Thus, \( x = -3 \) is indeed a solution to the quadratic equation \( -3x^2 - 9x = 0 \).