Z^6-3Z^3=8

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Solution for Z^6-3Z^3=8 equation: 


Simplifying
Z6 + -3Z3 = 8

Reorder the terms:
-3Z3 + Z6 = 8

Solving
-3Z3 + Z6 = 8

Solving for variable 'Z'.

Reorder the terms:
-8 + -3Z3 + Z6 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -3Z3 + Z6 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3Z3 + 8 + Z6 = 0 + 8

Reorder the terms:
-8 + 8 + -3Z3 + Z6 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3Z3 + Z6 = 0 + 8
-3Z3 + Z6 = 0 + 8

Combine like terms: 0 + 8 = 8
-3Z3 + Z6 = 8

The Z term is -3Z3.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3Z3 + 2.25 + Z6 = 8 + 2.25

Reorder the terms:
2.25 + -3Z3 + Z6 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + -3Z3 + Z6 = 10.25

Factor a perfect square on the left side:
(Z3 + -1.5)(Z3 + -1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(Z3 + -1.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
Z3 + -1.5 = 3.201562119

Simplifying
Z3 + -1.5 = 3.201562119

Reorder the terms:
-1.5 + Z3 = 3.201562119

Solving
-1.5 + Z3 = 3.201562119

Solving for variable 'Z'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + Z3 = 3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + Z3 = 3.201562119 + 1.5
Z3 = 3.201562119 + 1.5

Combine like terms: 3.201562119 + 1.5 = 4.701562119
Z3 = 4.701562119

Simplifying
Z3 = 4.701562119

Reorder the terms:
-4.701562119 + Z3 = 4.701562119 + -4.701562119

Combine like terms: 4.701562119 + -4.701562119 = 0.000000000
-4.701562119 + Z3 = 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
Z3 + -1.5 = -3.201562119

Simplifying
Z3 + -1.5 = -3.201562119

Reorder the terms:
-1.5 + Z3 = -3.201562119

Solving
-1.5 + Z3 = -3.201562119

Solving for variable 'Z'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + Z3 = -3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + Z3 = -3.201562119 + 1.5
Z3 = -3.201562119 + 1.5

Combine like terms: -3.201562119 + 1.5 = -1.701562119
Z3 = -1.701562119

Simplifying
Z3 = -1.701562119

Reorder the terms:
1.701562119 + Z3 = -1.701562119 + 1.701562119

Combine like terms: -1.701562119 + 1.701562119 = 0.000000000
1.701562119 + Z3 = 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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