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 values of x?

There are 12 numbers, so the median is the average of the 6th and 7th terms, which are (8x + 1) and (x² + 1). So [(8x + 1) + (x² + 1)]/2 = 25, giving x² + 8x + 2 = 50, i.e. x² + 8x − 48 = 0. Factoring: (x + 12)(x − 4) = 0, so x = −12 or x = 4. Both values must also keep the descending order valid, and checking each value, both satisfy the descending arrangement with the values fitting between 36 and 13.