The expression you provided is:

\[
x^2 - 7x + \frac{49}{4}
\]

This expression can be analyzed or simplified further. If you're looking to simplify it or express it in a different form, one approach is to complete the square. Let's do that:

### Completing the Square:
1. Start with the expression:
   \[
   x^2 - 7x + \frac{49}{4}
   \]

2. Split the middle term to assist in completing the square. The middle term is \(-7x\), which can be split as:
   \[
   x^2 - 7x = x^2 - 2\left(\frac{7}{2}\right)x
   \]

3. To complete the square, add and subtract \(\left(\frac{7}{2}\right)^2\) inside the expression:
   \[
   x^2 - 2\left(\frac{7}{2}\right)x + \left(\frac{7}{2}\right)^2 - \left(\frac{7}{2}\right)^2 + \frac{49}{4}
   \]

4. Simplify the expression:
   \[
   \left(x - \frac{7}{2}\right)^2 - \frac{49}{4} + \frac{49}{4}
   \]

5. The expression now simplifies to:
   \[
   \left(x - \frac{7}{2}\right)^2
   \]

### Final Answer:
The expression \(x^2 - 7x + \frac{49}{4}\) simplifies to:

\[
\left(x - \frac{7}{2}\right)^2
\]

This is a perfect square trinomial.

Would you like more details or have any other questions?

### Related Questions:
1. How do you complete the square for a quadratic expression?
2. What is the importance of completing the square in solving quadratic equations?
3. Can you solve the quadratic equation \(x^2 - 7x + \frac{49}{4} = 0\)?
4. How do you factor quadratic expressions of the form \(ax^2 + bx + c\)?
5. What are the applications of perfect square trinomials in algebra?

### Tip:
When completing the square, always remember to balance the equation by adding and subtracting the same value within the expression.

Learn how to complete the square for the quadratic expression x^2 - 7x + 49/4 with a step-by-step solution. This problem covers key algebraic concepts including completing the square and the quadratic formula theorem. Suitable for students in Grades 9-12.

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