+1839 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.
+129852 Simplify as
x^2 - 21x + y^2 + 13y = 25 complate 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 ] = 21/2 + sqrt [ 710 ] / 2
