A) x^{2}-2x-24 = (x-6)(x+4) = 0, x = 6,-4

B) for x^{2}+bx+c, a perfect square is (x+b/2)^{2} or (x-1)^{2} = x^{2}-2x+1. So we have to add 1 and subtract 1.

(x-1)^{2} -1 -24 = (x-1)^{2}-25=0

x-1 = ±√25 = ±5

x = 1±5 = 6, -4

C) x = (2±√(4-4(1)(-24)))/2 = (2 ± √100)/2 = 1 ±5 = 6,-4