Question

simplify (1/4x with an exponent of 2 - 3x + 2.25) + (0.75x with an exponent of 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 begin by combining like terms step by step.

1. **Identify the like terms:**
- Quadratic terms: \(\frac{1}{4}x^2\) and \(0.75x^2\)
- Linear terms: \(-3x\) and \(2x\)
- Constant terms: \(2.25\) and \(-\frac{1}{4}\)

2. **Combine the quadratic terms:**
\[
\frac{1}{4}x^2 + 0.75x^2 = \frac{1}{4}x^2 + \frac{3}{4}x^2 = 1x^2 = x^2
\]

3. **Combine the linear terms:**
\[
-3x + 2x = -1x = -x
\]

4. **Combine the constant terms:**
First, convert \(2.25\) to a fraction:
\[
2.25 = \frac{9}{4}
\]
Next, combine it with \(-\frac{1}{4}\):
\[
\frac{9}{4} - \frac{1}{4} = \frac{8}{4} = 2
\]

5. **Putting it all together:**
Now, we can express the final simplified form:
\[
x^2 - x + 2
\]

Thus, the simplified expression is:
\[
\boxed{x^2 - x + 2}
\]