K - 1 - 1/x = - sqrt(1/x**2 + 1)

K**2 - 2K - 2K/x + 1 + 2/x + 1/x**2 = 1/x**2 + 1
K**2 - 2K = (2K - 2)/x
x = 2(K-1)/(K**2 - 2K)