Set this equal to zero with the x^4 term positive by adding x^4 -200 to each side:
0=x^4 +102x^2 -200.
Now, are you sure you copied this problem correctly, because if the signs had been different, it would have factored nicely. If it had been x^4 +200 = 102x^2, then it would have factored. By subtracting 102x^2 from each side you get:
x^4 -102x^2+ 200 = 0
(x^2 - 100)(x^2-2) = 0
From this there will be two possibilities, each of which has two solutions:
x^2 - 100 = 0
x^2 = 100
x= 10 or x = -10
The second possibility is
x^2 - 2 = 0
x^2 = 2 or
If the problem was correctly stated, then the quadratic formula or completing the square method must be applied.
