x^4+2x^2-100=0

Solution for x^4+2x^2-100=0 equation:

Simplifying
x4 + 2x2 + -100 = 0

Reorder the terms:
-100 + 2x2 + x4 = 0

Solving
-100 + 2x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 2x2 + 100 + x4 = 0 + 100

Reorder the terms:
-100 + 100 + 2x2 + x4 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 2x2 + x4 = 0 + 100
2x2 + x4 = 0 + 100

Combine like terms: 0 + 100 = 100
2x2 + x4 = 100

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = 100 + 1

Reorder the terms:
1 + 2x2 + x4 = 100 + 1

Combine like terms: 100 + 1 = 101
1 + 2x2 + x4 = 101

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(x2 + 1) equal to 10.049875621 and -10.049875621.

Subproblem 1
x2 + 1 = 10.049875621

Simplifying
x2 + 1 = 10.049875621

Reorder the terms:
1 + x2 = 10.049875621

Solving
1 + x2 = 10.049875621

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x2 = 10.049875621 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 10.049875621 + -1
x2 = 10.049875621 + -1

Combine like terms: 10.049875621 + -1 = 9.049875621
x2 = 9.049875621

Simplifying
x2 = 9.049875621

Take the square root of each side:
x = {-3.008301119, 3.008301119}

Subproblem 2
x2 + 1 = -10.049875621

Simplifying
x2 + 1 = -10.049875621

Reorder the terms:
1 + x2 = -10.049875621

Solving
1 + x2 = -10.049875621

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x2 = -10.049875621 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = -10.049875621 + -1
x2 = -10.049875621 + -1

Combine like terms: -10.049875621 + -1 = -11.049875621
x2 = -11.049875621

Simplifying
x2 = -11.049875621

Reorder the terms:
11.049875621 + x2 = -11.049875621 + 11.049875621

Combine like terms: -11.049875621 + 11.049875621 = 0.000000000
11.049875621 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.