x^6-13x^3+4=0

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Solution for x^6-13x^3+4=0 equation: 


Simplifying
x6 + -13x3 + 4 = 0

Reorder the terms:
4 + -13x3 + x6 = 0

Solving
4 + -13x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -13x3 + -4 + x6 = 0 + -4

Reorder the terms:
4 + -4 + -13x3 + x6 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -13x3 + x6 = 0 + -4
-13x3 + x6 = 0 + -4

Combine like terms: 0 + -4 = -4
-13x3 + x6 = -4

The x term is -13x3.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x3 + 42.25 + x6 = -4 + 42.25

Reorder the terms:
42.25 + -13x3 + x6 = -4 + 42.25

Combine like terms: -4 + 42.25 = 38.25
42.25 + -13x3 + x6 = 38.25

Factor a perfect square on the left side:
(x3 + -6.5)(x3 + -6.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x3 + -6.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
x3 + -6.5 = 6.184658438

Simplifying
x3 + -6.5 = 6.184658438

Reorder the terms:
-6.5 + x3 = 6.184658438

Solving
-6.5 + x3 = 6.184658438

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x3 = 6.184658438 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x3 = 6.184658438 + 6.5
x3 = 6.184658438 + 6.5

Combine like terms: 6.184658438 + 6.5 = 12.684658438
x3 = 12.684658438

Simplifying
x3 = 12.684658438

Reorder the terms:
-12.684658438 + x3 = 12.684658438 + -12.684658438

Combine like terms: 12.684658438 + -12.684658438 = 0.000000000
-12.684658438 + 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 + -6.5 = -6.184658438

Simplifying
x3 + -6.5 = -6.184658438

Reorder the terms:
-6.5 + x3 = -6.184658438

Solving
-6.5 + x3 = -6.184658438

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x3 = -6.184658438 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x3 = -6.184658438 + 6.5
x3 = -6.184658438 + 6.5

Combine like terms: -6.184658438 + 6.5 = 0.315341562
x3 = 0.315341562

Simplifying
x3 = 0.315341562

Reorder the terms:
-0.315341562 + x3 = 0.315341562 + -0.315341562

Combine like terms: 0.315341562 + -0.315341562 = 0.000000000
-0.315341562 + 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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