1.
2x^2 - 4x + 16 = 0 divide through by 2
x^2 - 2x + 8 = 0 complete the square on x
x^2 - 2x + 1 = - 8 + 1
(x - 1)^2 = - 7
x - 1 = ±√-7
x = ± i√7 + 1
The second answer is correct
2.
Here are the answers that go into each box
x^4 + 2x^2y^2 + y^4
x^4 + 4x^2y^2
x^2 (x^2 + 4y^2)