x^4+100x^2=10000

Solution for x^4+100x^2=10000 equation:

Simplifying
x4 + 100x2 = 10000

Reorder the terms:
100x2 + x4 = 10000

Solving
100x2 + x4 = 10000

Solving for variable 'x'.

Reorder the terms:
-10000 + 100x2 + x4 = 10000 + -10000

Combine like terms: 10000 + -10000 = 0
-10000 + 100x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '10000' to each side of the equation.
-10000 + 100x2 + 10000 + x4 = 0 + 10000

Reorder the terms:
-10000 + 10000 + 100x2 + x4 = 0 + 10000

Combine like terms: -10000 + 10000 = 0
0 + 100x2 + x4 = 0 + 10000
100x2 + x4 = 0 + 10000

Combine like terms: 0 + 10000 = 10000
100x2 + x4 = 10000

The x term is 100x2.  Take half its coefficient (50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
100x2 + 2500 + x4 = 10000 + 2500

Reorder the terms:
2500 + 100x2 + x4 = 10000 + 2500

Combine like terms: 10000 + 2500 = 12500
2500 + 100x2 + x4 = 12500

Factor a perfect square on the left side:
(x2 + 50)(x2 + 50) = 12500

Calculate the square root of the right side: 111.803398875

Break this problem into two subproblems by setting 
(x2 + 50) equal to 111.803398875 and -111.803398875.

Subproblem 1
x2 + 50 = 111.803398875

Simplifying
x2 + 50 = 111.803398875

Reorder the terms:
50 + x2 = 111.803398875

Solving
50 + x2 = 111.803398875

Solving for variable 'x'.

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

Add '-50' to each side of the equation.
50 + -50 + x2 = 111.803398875 + -50

Combine like terms: 50 + -50 = 0
0 + x2 = 111.803398875 + -50
x2 = 111.803398875 + -50

Combine like terms: 111.803398875 + -50 = 61.803398875
x2 = 61.803398875

Simplifying
x2 = 61.803398875

Take the square root of each side:
x = {-7.861513778, 7.861513778}

Subproblem 2
x2 + 50 = -111.803398875

Simplifying
x2 + 50 = -111.803398875

Reorder the terms:
50 + x2 = -111.803398875

Solving
50 + x2 = -111.803398875

Solving for variable 'x'.

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

Add '-50' to each side of the equation.
50 + -50 + x2 = -111.803398875 + -50

Combine like terms: 50 + -50 = 0
0 + x2 = -111.803398875 + -50
x2 = -111.803398875 + -50

Combine like terms: -111.803398875 + -50 = -161.803398875
x2 = -161.803398875

Simplifying
x2 = -161.803398875

Reorder the terms:
161.803398875 + x2 = -161.803398875 + 161.803398875

Combine like terms: -161.803398875 + 161.803398875 = 0.000000000
161.803398875 + 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.