Solve : `x^(2) = {x}`, where `{x}` represents the fractional part function.

Explanation

To solve the equation \( x^2 = \{x\} \), where \( \{x\} \) represents the fractional part of \( x \), we can follow these steps:

### Step 1: Understand the fractional part function
The fractional part function \( \{x\} \) is defined as:
\[ \{x\} = x - \lfloor x \rfloor \]
where \( \lfloor x \rfloor \) is the greatest integer less than or equal to \( x \). This means that \( \{x\} \) takes values in the interval \([0, 1)\).
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