x^8-34x^4+104=0

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Solution for x^8-34x^4+104=0 equation: 


Simplifying
x8 + -34x4 + 104 = 0

Reorder the terms:
104 + -34x4 + x8 = 0

Solving
104 + -34x4 + x8 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-104' to each side of the equation.
104 + -34x4 + -104 + x8 = 0 + -104

Reorder the terms:
104 + -104 + -34x4 + x8 = 0 + -104

Combine like terms: 104 + -104 = 0
0 + -34x4 + x8 = 0 + -104
-34x4 + x8 = 0 + -104

Combine like terms: 0 + -104 = -104
-34x4 + x8 = -104

The x term is -34x4.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34x4 + 289 + x8 = -104 + 289

Reorder the terms:
289 + -34x4 + x8 = -104 + 289

Combine like terms: -104 + 289 = 185
289 + -34x4 + x8 = 185

Factor a perfect square on the left side:
(x4 + -17)(x4 + -17) = 185

Calculate the square root of the right side: 13.601470509

Break this problem into two subproblems by setting 
(x4 + -17) equal to 13.601470509 and -13.601470509.


Subproblem 1
x4 + -17 = 13.601470509

Simplifying
x4 + -17 = 13.601470509

Reorder the terms:
-17 + x4 = 13.601470509

Solving
-17 + x4 = 13.601470509

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + x4 = 13.601470509 + 17

Combine like terms: -17 + 17 = 0
0 + x4 = 13.601470509 + 17
x4 = 13.601470509 + 17

Combine like terms: 13.601470509 + 17 = 30.601470509
x4 = 30.601470509

Simplifying
x4 = 30.601470509

Reorder the terms:
-30.601470509 + x4 = 30.601470509 + -30.601470509

Combine like terms: 30.601470509 + -30.601470509 = 0.000000000
-30.601470509 + 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 + -17 = -13.601470509

Simplifying
x4 + -17 = -13.601470509

Reorder the terms:
-17 + x4 = -13.601470509

Solving
-17 + x4 = -13.601470509

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + x4 = -13.601470509 + 17

Combine like terms: -17 + 17 = 0
0 + x4 = -13.601470509 + 17
x4 = -13.601470509 + 17

Combine like terms: -13.601470509 + 17 = 3.398529491
x4 = 3.398529491

Simplifying
x4 = 3.398529491

Reorder the terms:
-3.398529491 + x4 = 3.398529491 + -3.398529491

Combine like terms: 3.398529491 + -3.398529491 = 0.000000000
-3.398529491 + 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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