x^2 -14x + y^2 - 48y = 0
x^2 - 14x + 49 + y^2 - 48y + 576 = 49 + 576
(x - 7)^2 + ( y - 24)^2 = 625
x is minimized/maximized when y = 24
(x - 7)^2 = 625 take both roots
x - 7 = 25 or x - 7 = -25
x = 32 or x = - 18
So....x = -18 is the minimum value for x