# No Integer allowed

Algebra Level 5

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

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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