If x - y = 12 and y^2 = 5(x - 2), what are the two possible values of x?
x - y = 12 → y = x - 12
So
y^2 = 5 ( x - 2)
(x -12)^2 = 5x - 10
x^2 -24x + 144 = 5x -10
x^2 - 24x - 5x + 144 + 10 = 0
x^2 - 29x + 154 = 0 factor
(x - 22) ( x - 7) = 0
Set both factors to 0 and solve for x
x = 22 or x = 7
