Exponential and Power Function Together?

$x^2=2^x$ 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 $P$ ).