Given a trapezoid ABCD, AB = CD = 26, BC = 22, AD = 42, the AC diagonal is equal to x. Find x.

Since by the condition AB = CD = 26, the trapezoid ABCD is isosceles, and the sides AB and CD are the lateral sides.
The length of the diagonal of an isosceles trapezoid is found by the formula:
d = √ (ab + c ^ 2),
where a is the length of the larger base, b is the length of the smaller base, c is the length of the lateral side of the trapezoid.
According to the condition, the values are given: a = 42, b = 22, c = 26. Substitute these values into the formula and find the length of the AC diagonal:
AC = √ (AD * BC + AB ^ 2) = √ (42 * 22 + 26 ^ 2) = √ (924 + 676) = √1600 = 40.
Since the trapezoid is isosceles by condition, both of its diagonals are equal: AC = BD.
Answer: AC = x = 40.