Question

Simplify: (1/4 x^2 - 3x +2.25) + (0.75x^2 + 2x - 1/4)

Answer 1

To simplify the expression \((\frac{1}{4} x^2 - 3x + 2.25) + (0.75x^2 + 2x - \frac{1}{4})\), we will combine like terms.

1. **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:
\[
\frac{1}{4} x^2 + \frac{3}{4} x^2 = \frac{1 + 3}{4} x^2 = \frac{4}{4} x^2 = x^2.
\]

2. **Combine \(x\) terms:**
- The first part has \(-3x\).
- The second part has \(2x\).

Adding these gives:
\[
-3x + 2x = -1x = -x.
\]

3. **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:
\[
\boxed{x^2 - x + 2}.
\]