x^2 + y^2 = 53 x^2 + (9 - x)^2 = 53 Remove the brackets. x^2 + 81 - 18x + x^2 = 53 Collect the like terms on the left. 2x^2 - 18x + 81 = 53 Subtract 53 from both sides. 2x^2 - 18x + 81 - 53 = 0 2x^2 - 18x + 28 = 0 This factors, but you can see it much easier if you pull out 2 as a common factor. 2(x^2 - 9x + 14) = 0 2(x - 2)(x - 7) =0 You could divide by 2 on both sides. But you can also leave it. x - 2 = 0 x = 2 x - 7 = 0 x = 7 If x = 2 then y = 7 If x = 7 then y = 2
