To simplify the expression \( (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \), we start by combining like terms.
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Combine the \(x^2\) terms: \[ 14x^2 + 0.75x^2 = (14 + 0.75)x^2 = 14.75x^2 \]
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Combine the \(x\) terms: \[ -3x + 2x = (-3 + 2)x = -1x = -x \]
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Combine the constant terms: \[ 2.25 - 14 = 2.25 - 14 = -11.75 \]
Now we can put it all together: \[ 14.75x^2 - x - 11.75 \]
Thus, the sum of the polynomials is: \[ \boxed{14.75x^2 - x - 11.75} \]