SOLUTION: |x^2 - 4x - 4 | = 8

|x^2 - 4x - 4 | = 8    (1)


The equation (1) is equivalent to this:


    Find the solution set to this set of equations:

        EITHER   x^2 - 4x - 4 = 8       (2)
        OR       x^2 - 4x - 4 = -8.     (3)


Notice that these two equations, (2) and (3), are connected by the logical term "OR",

which means that the set of solutions to equation (1)  is the UNION  of solutions to equations  (2)  and (3).


Now,

    x^2 - 4x - 4 = 8   ====>  x^2 - 4x - 12 = 0  ====>  (x+2)\*(c-6) = 0  ====>  the solutions are  x = -2  and/or  x = 6,

and

    x^2 - 4x - 4 = -8  ====>  x^2 - 4x + 4 = 0  ====>  (x-2)^2 = 0  ====>  the solution is  x = 2.


Thus the solution to the given equation (1) is the set  {-2, 2, 6}.