x^6-5x^3-8=0

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Solution for x^6-5x^3-8=0 equation:


Simplifying
x6 + -5x3 + -8 = 0

Reorder the terms:
-8 + -5x3 + x6 = 0

Solving
-8 + -5x3 + 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 + -5x3 + 8 + x6 = 0 + 8

Reorder the terms:
-8 + 8 + -5x3 + x6 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x3 + x6 = 0 + 8
-5x3 + x6 = 0 + 8

Combine like terms: 0 + 8 = 8
-5x3 + x6 = 8

The x term is -5x3.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x3 + 6.25 + x6 = 8 + 6.25

Reorder the terms:
6.25 + -5x3 + x6 = 8 + 6.25

Combine like terms: 8 + 6.25 = 14.25
6.25 + -5x3 + x6 = 14.25

Factor a perfect square on the left side:
(x3 + -2.5)(x3 + -2.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x3 + -2.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x3 + -2.5 = 3.774917218 Simplifying x3 + -2.5 = 3.774917218 Reorder the terms: -2.5 + x3 = 3.774917218 Solving -2.5 + x3 = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x3 = 3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x3 = 3.774917218 + 2.5 x3 = 3.774917218 + 2.5 Combine like terms: 3.774917218 + 2.5 = 6.274917218 x3 = 6.274917218 Simplifying x3 = 6.274917218 Reorder the terms: -6.274917218 + x3 = 6.274917218 + -6.274917218 Combine like terms: 6.274917218 + -6.274917218 = 0.000000000 -6.274917218 + 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 + -2.5 = -3.774917218 Simplifying x3 + -2.5 = -3.774917218 Reorder the terms: -2.5 + x3 = -3.774917218 Solving -2.5 + x3 = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x3 = -3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x3 = -3.774917218 + 2.5 x3 = -3.774917218 + 2.5 Combine like terms: -3.774917218 + 2.5 = -1.274917218 x3 = -1.274917218 Simplifying x3 = -1.274917218 Reorder the terms: 1.274917218 + x3 = -1.274917218 + 1.274917218 Combine like terms: -1.274917218 + 1.274917218 = 0.000000000 1.274917218 + 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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