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.
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Substitute \( x = -3 \) into the equation: \[ -3(-3)^2 - 9(-3) = 0 \]
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Calculate \( (-3)^2 \): \[ (-3)^2 = 9 \]
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Multiply by -3: \[ -3 \cdot 9 = -27 \]
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Calculate \( -9 \cdot (-3) \): \[ -9 \cdot -3 = 27 \]
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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 \( -3x^2 - 9x = 0 \).