Let x and y be real numbers. If x and y satisfy x^2+y^2=4x+6y+15, then find the largest possible value of x. Give your answer in exact form using radicals, simplified as far as possible. Thanks!
x^2 - 4x + y^2 - 6y = 15 complete the square on x,y
x^2 -4x + 4 + y^2 -6y + 9 = 15 + 4 + 9
(x -2)^2 + (y - 3)^2 = 28
This is a circle centered at (2, 3) with a radius of sqrt (28) = 2sqrt 7
Largest value for x = 2 + 2sqrt(7)
+101 
