A circle is centered at (5,15) and has a radius of sqrt130 units. Point Q = (x,y) is on the circle, has integer coordinates, and the value of the x-coordinate is equal to the value of the y-coordinate. What is the maximum possible value for x?
+128472 Since x = y , need to solve this
(x - 5)^2 + ( x - 15)^2 = 130
x^2 - 10x + 25 + x^2 - 30x + 225 = 130
2x^2 -40x + 120 = 0 divide through by 2
x^2 - 20x + 60 = 0
x^2 - 20x = - 60 complete the square on x
x^2 -20x + 100 = -60 + 100
(x - 10)^2 = 40 take the positive root
x -10 = sqrt (40)
x = 10 + sqrt (40) = 10 + 2sqrt (10) ≈ 16.325
