MathNet 1985 — Part 01 Question 33

$x$ is a real number. Define $x_0 = 1 + \sqrt{1 + x}$, $x_1 = 2 + x / x_0$, $x_2 = 2 + x / x_1$, ..., $x_{1985} = 2 + x / x_{1984}$. Find all solutions to $x_{1985} = x$.