# Exponential and Power Function Together?

Calculus Level 4

$$x^2=2^x$$ has integral solutions $$x=2 \text{ or } 4$$, but it also has one other negative, real solution. If $$P$$ is this solution, what is the absolute value of $$\lfloor 10^7 \times P \rfloor$$?

You may use a calculator only for indirect calculations (i.e., not directly finding $$P$$).

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