Let $x$ be the minimal root of the equation $x^2 - 4x + 2 = 0$. Find the first two digits after the decimal point of the number $\{x + x^2 + \cdots + x^{20}\}$, where $\{a\}$ denotes the fractional part of $a$.

Let's think step by step and output the final answer within \boxed{}.
user