Find all solutions of the equation \(|x^2-30x-1|=30.\)
Note....either l a l = 30 or l -a l = 30
x^2 - 30x - 1 = 30
x^2 -30x - 31 = 0
(x -31) ( x + 1) = 0
x = 31 and x = -1
Also
- (x^2 - 30x - 1) = 30
-x^2 + 30x + 1 = 30
x^2 - 30x - 1 = -30
x^2 - 30x + 29 = 0
( x - 1) ( x -29) = 0
x = 1 and x = 29
