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 will follow a systematic approach.

### Step 1: Understand the fractional part function
The fractional part function \( \{x\} \) is defined as:
\[ \{x\} = x - \lfloor x \rfloor \]
This means that \( \{x\} \) gives the decimal part of \( x \) and is always in the range \( [0, 1) \).
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