x^6-35x^3+27=0

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Solution for x^6-35x^3+27=0 equation: 


Simplifying
x6 + -35x3 + 27 = 0

Reorder the terms:
27 + -35x3 + x6 = 0

Solving
27 + -35x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -35x3 + -27 + x6 = 0 + -27

Reorder the terms:
27 + -27 + -35x3 + x6 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -35x3 + x6 = 0 + -27
-35x3 + x6 = 0 + -27

Combine like terms: 0 + -27 = -27
-35x3 + x6 = -27

The x term is -35x3.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x3 + 306.25 + x6 = -27 + 306.25

Reorder the terms:
306.25 + -35x3 + x6 = -27 + 306.25

Combine like terms: -27 + 306.25 = 279.25
306.25 + -35x3 + x6 = 279.25

Factor a perfect square on the left side:
(x3 + -17.5)(x3 + -17.5) = 279.25

Calculate the square root of the right side: 16.710774967

Break this problem into two subproblems by setting 
(x3 + -17.5) equal to 16.710774967 and -16.710774967.


Subproblem 1
x3 + -17.5 = 16.710774967

Simplifying
x3 + -17.5 = 16.710774967

Reorder the terms:
-17.5 + x3 = 16.710774967

Solving
-17.5 + x3 = 16.710774967

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x3 = 16.710774967 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x3 = 16.710774967 + 17.5
x3 = 16.710774967 + 17.5

Combine like terms: 16.710774967 + 17.5 = 34.210774967
x3 = 34.210774967

Simplifying
x3 = 34.210774967

Reorder the terms:
-34.210774967 + x3 = 34.210774967 + -34.210774967

Combine like terms: 34.210774967 + -34.210774967 = 0.000000000
-34.210774967 + x3 = 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
x3 + -17.5 = -16.710774967

Simplifying
x3 + -17.5 = -16.710774967

Reorder the terms:
-17.5 + x3 = -16.710774967

Solving
-17.5 + x3 = -16.710774967

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x3 = -16.710774967 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x3 = -16.710774967 + 17.5
x3 = -16.710774967 + 17.5

Combine like terms: -16.710774967 + 17.5 = 0.789225033
x3 = 0.789225033

Simplifying
x3 = 0.789225033

Reorder the terms:
-0.789225033 + x3 = 0.789225033 + -0.789225033

Combine like terms: 0.789225033 + -0.789225033 = 0.000000000
-0.789225033 + x3 = 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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