To find the value of the expression \( 10x^2 - 3x - 6 \) when \( x = 3 \), we will substitute 3 for \( x \) in the expression.
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Substitute \( x = 3 \): \[ 10(3)^2 - 3(3) - 6 \]
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Calculate \( 10(3)^2 \): \[ 10 \times 9 = 90 \]
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Calculate \( -3(3) \): \[ -9 \]
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Now substitute these values back into the expression: \[ 90 - 9 - 6 \]
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Perform the subtraction: \[ 90 - 9 = 81 \] \[ 81 - 6 = 75 \]
Thus, the value of the expression \( 10x^2 - 3x - 6 \) when \( x = 3 \) is \( \boxed{75} \).