x^8+36x^4+81=0

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Solution for x^8+36x^4+81=0 equation: 


Simplifying
x8 + 36x4 + 81 = 0

Reorder the terms:
81 + 36x4 + x8 = 0

Solving
81 + 36x4 + x8 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + 36x4 + -81 + x8 = 0 + -81

Reorder the terms:
81 + -81 + 36x4 + x8 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + 36x4 + x8 = 0 + -81
36x4 + x8 = 0 + -81

Combine like terms: 0 + -81 = -81
36x4 + x8 = -81

The x term is 36x4.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x4 + 324 + x8 = -81 + 324

Reorder the terms:
324 + 36x4 + x8 = -81 + 324

Combine like terms: -81 + 324 = 243
324 + 36x4 + x8 = 243

Factor a perfect square on the left side:
(x4 + 18)(x4 + 18) = 243

Calculate the square root of the right side: 15.588457268

Break this problem into two subproblems by setting 
(x4 + 18) equal to 15.588457268 and -15.588457268.


Subproblem 1
x4 + 18 = 15.588457268

Simplifying
x4 + 18 = 15.588457268

Reorder the terms:
18 + x4 = 15.588457268

Solving
18 + x4 = 15.588457268

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x4 = 15.588457268 + -18

Combine like terms: 18 + -18 = 0
0 + x4 = 15.588457268 + -18
x4 = 15.588457268 + -18

Combine like terms: 15.588457268 + -18 = -2.411542732
x4 = -2.411542732

Simplifying
x4 = -2.411542732

Reorder the terms:
2.411542732 + x4 = -2.411542732 + 2.411542732

Combine like terms: -2.411542732 + 2.411542732 = 0.000000000
2.411542732 + x4 = 0.000000000

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


Subproblem 2
x4 + 18 = -15.588457268

Simplifying
x4 + 18 = -15.588457268

Reorder the terms:
18 + x4 = -15.588457268

Solving
18 + x4 = -15.588457268

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x4 = -15.588457268 + -18

Combine like terms: 18 + -18 = 0
0 + x4 = -15.588457268 + -18
x4 = -15.588457268 + -18

Combine like terms: -15.588457268 + -18 = -33.588457268
x4 = -33.588457268

Simplifying
x4 = -33.588457268

Reorder the terms:
33.588457268 + x4 = -33.588457268 + 33.588457268

Combine like terms: -33.588457268 + 33.588457268 = 0.000000000
33.588457268 + x4 = 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.

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