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

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


Simplifying
8x6 + x3 + -20 = 0

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

Solving
-20 + x3 + 8x6 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-2.5 + 0.125x3 + x6 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.125x3 + 2.5 + x6 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.125x3 + x6 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.125x3 + x6 = 0 + 2.5
0.125x3 + x6 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.125x3 + x6 = 2.5

The x term is x3.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.125x3 + 0.25 + x6 = 2.5 + 0.25

Reorder the terms:
0.25 + 0.125x3 + x6 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
0.25 + 0.125x3 + x6 = 2.75

Factor a perfect square on the left side:
(x3 + 0.5)(x3 + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x3 + 0.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
x3 + 0.5 = 1.658312395

Simplifying
x3 + 0.5 = 1.658312395

Reorder the terms:
0.5 + x3 = 1.658312395

Solving
0.5 + x3 = 1.658312395

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x3 = 1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x3 = 1.658312395 + -0.5
x3 = 1.658312395 + -0.5

Combine like terms: 1.658312395 + -0.5 = 1.158312395
x3 = 1.158312395

Simplifying
x3 = 1.158312395

Reorder the terms:
-1.158312395 + x3 = 1.158312395 + -1.158312395

Combine like terms: 1.158312395 + -1.158312395 = 0.000000000
-1.158312395 + 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 + 0.5 = -1.658312395

Simplifying
x3 + 0.5 = -1.658312395

Reorder the terms:
0.5 + x3 = -1.658312395

Solving
0.5 + x3 = -1.658312395

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x3 = -1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x3 = -1.658312395 + -0.5
x3 = -1.658312395 + -0.5

Combine like terms: -1.658312395 + -0.5 = -2.158312395
x3 = -2.158312395

Simplifying
x3 = -2.158312395

Reorder the terms:
2.158312395 + x3 = -2.158312395 + 2.158312395

Combine like terms: -2.158312395 + 2.158312395 = 0.000000000
2.158312395 + 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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