z^8-17z^4-16=0

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Solution for z^8-17z^4-16=0 equation: 


Simplifying
z8 + -17z4 + -16 = 0

Reorder the terms:
-16 + -17z4 + z8 = 0

Solving
-16 + -17z4 + z8 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -17z4 + 16 + z8 = 0 + 16

Reorder the terms:
-16 + 16 + -17z4 + z8 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -17z4 + z8 = 0 + 16
-17z4 + z8 = 0 + 16

Combine like terms: 0 + 16 = 16
-17z4 + z8 = 16

The z term is -17z4.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17z4 + 72.25 + z8 = 16 + 72.25

Reorder the terms:
72.25 + -17z4 + z8 = 16 + 72.25

Combine like terms: 16 + 72.25 = 88.25
72.25 + -17z4 + z8 = 88.25

Factor a perfect square on the left side:
(z4 + -8.5)(z4 + -8.5) = 88.25

Calculate the square root of the right side: 9.394147114

Break this problem into two subproblems by setting 
(z4 + -8.5) equal to 9.394147114 and -9.394147114.


Subproblem 1
z4 + -8.5 = 9.394147114

Simplifying
z4 + -8.5 = 9.394147114

Reorder the terms:
-8.5 + z4 = 9.394147114

Solving
-8.5 + z4 = 9.394147114

Solving for variable 'z'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + z4 = 9.394147114 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + z4 = 9.394147114 + 8.5
z4 = 9.394147114 + 8.5

Combine like terms: 9.394147114 + 8.5 = 17.894147114
z4 = 17.894147114

Simplifying
z4 = 17.894147114

Reorder the terms:
-17.894147114 + z4 = 17.894147114 + -17.894147114

Combine like terms: 17.894147114 + -17.894147114 = 0.000000000
-17.894147114 + z4 = 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
z4 + -8.5 = -9.394147114

Simplifying
z4 + -8.5 = -9.394147114

Reorder the terms:
-8.5 + z4 = -9.394147114

Solving
-8.5 + z4 = -9.394147114

Solving for variable 'z'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + z4 = -9.394147114 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + z4 = -9.394147114 + 8.5
z4 = -9.394147114 + 8.5

Combine like terms: -9.394147114 + 8.5 = -0.894147114
z4 = -0.894147114

Simplifying
z4 = -0.894147114

Reorder the terms:
0.894147114 + z4 = -0.894147114 + 0.894147114

Combine like terms: -0.894147114 + 0.894147114 = 0.000000000
0.894147114 + z4 = 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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