Question

Simplify 1/4 x squared - 3x + 2.25 + 0.75x plus 2x - 1/4

Answer 1

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

1. **Identify the terms:**
- The quadratic term: \( \frac{1}{4}x^2 \)
- The linear terms: \( -3x + 0.75x + 2x \)
- The constant terms: \( 2.25 - \frac{1}{4} \)

2. **Combine the linear terms:**
\[
-3x + 0.75x + 2x = (-3 + 0.75 + 2)x = -3 + 2.75 = -0.25x
\]

3. **Combine the constant terms:**
- Convert \( 2.25 \) to a fraction: \( 2.25 = \frac{9}{4} \)
- We find a common denominator to combine:
\( 2.25 - \frac{1}{4} = \frac{9}{4} - \frac{1}{4} = \frac{8}{4} = 2 \)

4. **Putting it all together:**
\[
\frac{1}{4}x^2 - 0.25x + 2
\]

Thus, the simplified expression is:
\[
\frac{1}{4}x^2 - 0.25x + 2
\]