x^6+20x^3-8=0

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Solution for x^6+20x^3-8=0 equation: 


Simplifying
x6 + 20x3 + -8 = 0

Reorder the terms:
-8 + 20x3 + x6 = 0

Solving
-8 + 20x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 20x3 + 8 + x6 = 0 + 8

Reorder the terms:
-8 + 8 + 20x3 + x6 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 20x3 + x6 = 0 + 8
20x3 + x6 = 0 + 8

Combine like terms: 0 + 8 = 8
20x3 + x6 = 8

The x term is 20x3.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x3 + 100 + x6 = 8 + 100

Reorder the terms:
100 + 20x3 + x6 = 8 + 100

Combine like terms: 8 + 100 = 108
100 + 20x3 + x6 = 108

Factor a perfect square on the left side:
(x3 + 10)(x3 + 10) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(x3 + 10) equal to 10.392304845 and -10.392304845.


Subproblem 1
x3 + 10 = 10.392304845

Simplifying
x3 + 10 = 10.392304845

Reorder the terms:
10 + x3 = 10.392304845

Solving
10 + x3 = 10.392304845

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x3 = 10.392304845 + -10

Combine like terms: 10 + -10 = 0
0 + x3 = 10.392304845 + -10
x3 = 10.392304845 + -10

Combine like terms: 10.392304845 + -10 = 0.392304845
x3 = 0.392304845

Simplifying
x3 = 0.392304845

Reorder the terms:
-0.392304845 + x3 = 0.392304845 + -0.392304845

Combine like terms: 0.392304845 + -0.392304845 = 0.000000000
-0.392304845 + 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 + 10 = -10.392304845

Simplifying
x3 + 10 = -10.392304845

Reorder the terms:
10 + x3 = -10.392304845

Solving
10 + x3 = -10.392304845

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x3 = -10.392304845 + -10

Combine like terms: 10 + -10 = 0
0 + x3 = -10.392304845 + -10
x3 = -10.392304845 + -10

Combine like terms: -10.392304845 + -10 = -20.392304845
x3 = -20.392304845

Simplifying
x3 = -20.392304845

Reorder the terms:
20.392304845 + x3 = -20.392304845 + 20.392304845

Combine like terms: -20.392304845 + 20.392304845 = 0.000000000
20.392304845 + 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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