Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy x^2 + y^2 = 4x + 2y then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.
x^2 - 4x + y^2 - 2y = 0
x^2 - 4x + 4 + y^2 - 2y + 1 = 5
(x - 2)^2 + (y - 1)^2 = 5
This is a circle centered at (2, 1) with a radius of sqrt (5)
x max = 2 + sqrt (5)
+1768 
