To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we will combine like terms.
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Combine the \(x^2\) terms: \[ 14x^2 + 0.75x^2 = 14.75x^2 \]
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Combine the \(x\) terms: \[ -3x + 2x = -1x \quad \text{or simply} \quad -x \]
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Combine the constant terms: \[ 2.25 - 14 = -11.75 \]
Now, putting it all together, we have: \[ 14.75x^2 - x - 11.75 \]
Thus, the simplified form of the sum of the polynomials is: \[ \boxed{14.75x^2 - x - 11.75} \]
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