x^4+12x^2-100=0

Solution for x^4+12x^2-100=0 equation:

Simplifying
x4 + 12x2 + -100 = 0

Reorder the terms:
-100 + 12x2 + x4 = 0

Solving
-100 + 12x2 + 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 + 12x2 + 100 + x4 = 0 + 100

Reorder the terms:
-100 + 100 + 12x2 + x4 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 12x2 + x4 = 0 + 100
12x2 + x4 = 0 + 100

Combine like terms: 0 + 100 = 100
12x2 + x4 = 100

The x term is 12x2.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x2 + 36 + x4 = 100 + 36

Reorder the terms:
36 + 12x2 + x4 = 100 + 36

Combine like terms: 100 + 36 = 136
36 + 12x2 + x4 = 136

Factor a perfect square on the left side:
(x2 + 6)(x2 + 6) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(x2 + 6) equal to 11.66190379 and -11.66190379.

Subproblem 1
x2 + 6 = 11.66190379

Simplifying
x2 + 6 = 11.66190379

Reorder the terms:
6 + x2 = 11.66190379

Solving
6 + x2 = 11.66190379

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x2 = 11.66190379 + -6

Combine like terms: 6 + -6 = 0
0 + x2 = 11.66190379 + -6
x2 = 11.66190379 + -6

Combine like terms: 11.66190379 + -6 = 5.66190379
x2 = 5.66190379

Simplifying
x2 = 5.66190379

Take the square root of each side:
x = {-2.379475528, 2.379475528}

Subproblem 2
x2 + 6 = -11.66190379

Simplifying
x2 + 6 = -11.66190379

Reorder the terms:
6 + x2 = -11.66190379

Solving
6 + x2 = -11.66190379

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x2 = -11.66190379 + -6

Combine like terms: 6 + -6 = 0
0 + x2 = -11.66190379 + -6
x2 = -11.66190379 + -6

Combine like terms: -11.66190379 + -6 = -17.66190379
x2 = -17.66190379

Simplifying
x2 = -17.66190379

Reorder the terms:
17.66190379 + x2 = -17.66190379 + 17.66190379

Combine like terms: -17.66190379 + 17.66190379 = 0.00000000
17.66190379 + x2 = 0.00000000

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.