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