z^6-2z^3+4=0

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Solution for z^6-2z^3+4=0 equation:


Simplifying
z6 + -2z3 + 4 = 0

Reorder the terms:
4 + -2z3 + z6 = 0

Solving
4 + -2z3 + z6 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -2z3 + -4 + z6 = 0 + -4

Reorder the terms:
4 + -4 + -2z3 + z6 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2z3 + z6 = 0 + -4
-2z3 + z6 = 0 + -4

Combine like terms: 0 + -4 = -4
-2z3 + z6 = -4

The z term is -2z3.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z3 + 1 + z6 = -4 + 1

Reorder the terms:
1 + -2z3 + z6 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + -2z3 + z6 = -3

Factor a perfect square on the left side:
(z3 + -1)(z3 + -1) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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