x^6-7x^3+8=0

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Solution for x^6-7x^3+8=0 equation: 


Simplifying
x6 + -7x3 + 8 = 0

Reorder the terms:
8 + -7x3 + x6 = 0

Solving
8 + -7x3 + 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 + -7x3 + -8 + x6 = 0 + -8

Reorder the terms:
8 + -8 + -7x3 + x6 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x3 + x6 = 0 + -8
-7x3 + x6 = 0 + -8

Combine like terms: 0 + -8 = -8
-7x3 + x6 = -8

The x term is -7x3.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x3 + 12.25 + x6 = -8 + 12.25

Reorder the terms:
12.25 + -7x3 + x6 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7x3 + x6 = 4.25

Factor a perfect square on the left side:
(x3 + -3.5)(x3 + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x3 + -3.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x3 + -3.5 = 2.061552813

Simplifying
x3 + -3.5 = 2.061552813

Reorder the terms:
-3.5 + x3 = 2.061552813

Solving
-3.5 + x3 = 2.061552813

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x3 = 2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x3 = 2.061552813 + 3.5
x3 = 2.061552813 + 3.5

Combine like terms: 2.061552813 + 3.5 = 5.561552813
x3 = 5.561552813

Simplifying
x3 = 5.561552813

Reorder the terms:
-5.561552813 + x3 = 5.561552813 + -5.561552813

Combine like terms: 5.561552813 + -5.561552813 = 0.000000000
-5.561552813 + 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 + -3.5 = -2.061552813

Simplifying
x3 + -3.5 = -2.061552813

Reorder the terms:
-3.5 + x3 = -2.061552813

Solving
-3.5 + x3 = -2.061552813

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x3 = -2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x3 = -2.061552813 + 3.5
x3 = -2.061552813 + 3.5

Combine like terms: -2.061552813 + 3.5 = 1.438447187
x3 = 1.438447187

Simplifying
x3 = 1.438447187

Reorder the terms:
-1.438447187 + x3 = 1.438447187 + -1.438447187

Combine like terms: 1.438447187 + -1.438447187 = 0.000000000
-1.438447187 + 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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