+1588 Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
\[x^2 + y^2 = 4x - 8y + 17x - 5y + 25,\]
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.
+128578 x^2 - 21x + y^2 + 13y = 25 complete the square on x,y
x^2 - 21x + 441/4 + y^2 + 13y + 169/4 = 25 + 441/4 + 169/4
(x - 21/2)^2 + (y + 13/2)^2 = 355 / 2
This is a circle centered at (21/2 , -13/2) with a radius of sqrt (355 / 2)
Largest value of x = (21/2) + sqrt (355 / 2)
