+233 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.
+129630 Simplify as
x^2 -21x + y^2 + 13y = 25 complete the square on x and 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 = sqrt [ 355/2] = sqrt [ 710] / 2
The greatest value of x = 21/2 +sqrt (710 ) / 2 = [ 21 + sqrt 710 ] / 2
