To simplify the expression \((\frac{1}{4} x^2 - 3x + 2.25) + (0.75x^2 + 2x - \frac{1}{4})\), we will combine like terms.
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Combine \(x^2\) terms:
- The first part has \(\frac{1}{4} x^2\).
- The second part has \(0.75x^2\) which is equivalent to \(\frac{3}{4} x^2\).
Now, add these two: \[ \frac{1}{4} x^2 + \frac{3}{4} x^2 = \frac{1 + 3}{4} x^2 = \frac{4}{4} x^2 = x^2. \]
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Combine \(x\) terms:
- The first part has \(-3x\).
- The second part has \(2x\).
Adding these gives: \[ -3x + 2x = -1x = -x. \]
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Combine constant terms:
- The first part has \(2.25\) (which is \(\frac{9}{4}\)).
- The second part has \(-\frac{1}{4}\).
Adding these gives: \[ \frac{9}{4} - \frac{1}{4} = \frac{9 - 1}{4} = \frac{8}{4} = 2. \]
Now that we have combined all the like terms, the simplified expression is: \[ x^2 - x + 2. \]
Thus, the simplified expression is: \[ \boxed{x^2 - x + 2}. \]