To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we will combine like terms.
First, let's group the terms:
- Quadratic terms: \(14x^2 + 0.75x^2\)
- Linear terms: \(-3x + 2x\)
- Constant terms: \(2.25 - 14\)
Now, let's calculate each group:
1. **Quadratic terms**:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. **Linear terms**:
\[
-3x + 2x = -1x \quad \text{or simply } -x
\]
3. **Constant terms**:
\[
2.25 - 14 = -11.75
\]
Now, combine all these results:
\[
14.75x^2 - x - 11.75
\]
Thus, the simplified sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]