The expression you're looking at is \( x^2 - x + \frac{1}{4} \).

This expression can be factored or analyzed. It is a quadratic expression in the standard form \( ax^2 + bx + c \) where \( a = 1 \), \( b = -1 \), and \( c = \frac{1}{4} \).

1. **Factoring the expression**:
To factor \( x^2 - x + \frac{1}{4} \), you can notice that it can be rewritten as:
\[
\left( x - \frac{1}{2} \right)^2
\]

2. **Finding the roots**:
You can find the roots by setting the expression equal to zero:
\[
\left( x - \frac{1}{2} \right)^2 = 0
\]
This simplifies to \( x = \frac{1}{2} \) (a double root).

Thus, the expression \( x^2 - x + \frac{1}{4} \) can be represented in its factored form as:
\[
\left( x - \frac{1}{2} \right)^2
\]

Let me know if you need further information or help with this expression!