Differentiation doesn't work here

Find the smallest value of positive \(x\), that satisfies

\[ \large \lfloor x\rfloor^2 - x\lfloor x \rfloor +4 \leq 0 \]

Give your answer to 3 decimal places.

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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