To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we will combine like terms.
1. Group the terms:
- Quadratic terms: \(14x^2\) and \(0.75x^2\)
- Linear terms: \(-3x\) and \(2x\)
- Constant terms: \(2.25\) and \(-14\)
2. Combine the quadratic terms:
\[
14x^2 + 0.75x^2 = (14 + 0.75)x^2 = 14.75x^2
\]
3. Combine the linear terms:
\[
-3x + 2x = (-3 + 2)x = -1x = -x
\]
4. Combine the constant terms:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]
5. Putting it all together:
\[
14.75x^2 - x - 11.75
\]
Thus, the simplified expression is:
\[
\boxed{14.75x^2 - x - 11.75}
\]