There are two cases to consider:

Case 1: x1^2 - x2^2 = 15

In this case, we can factor the left-hand side as (x1 + x2)(x1 - x2) = 15. Since 15 is a prime number, the only possible pairs of factors are (1, 15) and (-1, -15), or their negatives. Solving for x1 and x2 in each case, we get the solutions:

• x1 = 8, x2 = -7
• x1 = -8, x2 = 7
• x1 = 4, x2 = -1
• x1 = -4, x2 = 1

Case 2: x2^2 - x1^2 = 15

This case is similar to Case 1, but with the signs of x1 and x2 switched. We can factor the left-hand side as (x2 + x1)(x2 - x1) = 15, and the only possible pairs of factors are (1, 15) and (-1, -15), or their negatives. Solving for x1 and x2 in each case, we get the solutions:

• x1 = -7, x2 = 8
• x1 = 7, x2 = -8
• x1 = -1, x2 = 4
• x1 = 1, x2 = -4

Therefore, the complete solution set for the equation | x1^2 - x2^2| = 15 is:

{(8, -7), (-8, 7), (4, -1), (-4, 1), (-7,????, (7, -8), (-1, 4), (1, -4)}