Z^4-4=0

Solution for Z^4-4=0 equation:

Simplifying
Z4 + -4 = 0

Reorder the terms:
-4 + Z4 = 0

Solving
-4 + Z4 = 0

Solving for variable 'Z'.

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

Add '4' to each side of the equation.
-4 + 4 + Z4 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + Z4 = 0 + 4
Z4 = 0 + 4

Combine like terms: 0 + 4 = 4
Z4 = 4

Simplifying
Z4 = 4

Reorder the terms:
-4 + Z4 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + Z4 = 0

Factor a difference between two squares.
(2 + Z2)(-2 + Z2) = 0

Subproblem 1
Set the factor '(2 + Z2)' equal to zero and attempt to solve:

Simplifying
2 + Z2 = 0

Solving
2 + Z2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + Z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + Z2 = 0 + -2
Z2 = 0 + -2

Combine like terms: 0 + -2 = -2
Z2 = -2

Simplifying
Z2 = -2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-2 + Z2)' equal to zero and attempt to solve:

Simplifying
-2 + Z2 = 0

Solving
-2 + Z2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + Z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + Z2 = 0 + 2
Z2 = 0 + 2

Combine like terms: 0 + 2 = 2
Z2 = 2

Simplifying
Z2 = 2

Take the square root of each side:
Z = {-1.414213562, 1.414213562}
Solution
Z = {-1.414213562, 1.414213562}