The numbers 59, 53, 51, 43, 36, (8x + 1), (x² + 1), 13, 12, 9, 7, 3 are written in descending order and their median is 25. What is/are the value(s) of x?

There are 12 numbers; median = average of 6th and 7th values. In descending order, the 6th and 7th are (8x+1) and (x²+1). So [(8x+1) + (x²+1)]/2 = 25, giving x² + 8x + 2 = 50, i.e., x² + 8x - 48 = 0, so (x+12)(x-4) = 0, x = -12 or 4. Check ordering constraint: the sequence must remain descending, so 36 ≥ 8x+1 ≥ x²+1 ≥ 13. For x = 4: 8x+1 = 33, x²+1 = 17 — sequence 36, 33, 17, 13 is descending ✓. For x = -12: 8x+1 = -95, which is not between 36 and 13 — violates ordering. So only x = 4 is valid.