There are no "real" solutions, just "complex" ones:
x = 1 - i sqrt(22) ≈ 1.00000 - 4.69042 i and y = 1 + i sqrt(22) ≈ 1.00000 + 4.69042 i
x = 1 + i sqrt(22) ≈ 1.00000 + 4.69042 i and y = 1 - i sqrt(22) ≈ 1.00000 - 4.69042 i
So that: ( 1 + i sqrt(22))^2 + (1 - i sqrt(22))^2
Simplify the following:
(i sqrt(22) + 1)^2 + (-(i sqrt(22)) + 1)^2
(i sqrt(22) + 1)^2 = 1 + i sqrt(22) + i sqrt(22) - 22 = 2 i sqrt(22) - 21:
2 i sqrt(22) - 21 + (-(i sqrt(22)) + 1)^2
(-(i sqrt(22)) + 1)^2 = 1 - i sqrt(22) - i sqrt(22) - 22 = -2 i sqrt(22) - 21:
-21 + 2 i sqrt(22) + -2 i sqrt(22) - 21
-21 + 2 i sqrt(22) - 21 - 2 i sqrt(22) = -42:
Answer: | -42