\[ \large 9 + \left\lfloor x \right\rfloor ^2 + \left\lfloor 2x \right\rfloor ^2 = \left\lfloor x^2 \right\rfloor + \left\lfloor (2x)^2 \right\rfloor \]

Let \(x_{\text{max}} \) denote the maximum value of \(x\) in the interval \(0 < x< 10\) that satisfy the equation above. Find \( \lfloor 100 x_{\text{max}} \rfloor \).

You might need a calculator for the final step of your working.

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