z^4=10000

Solution for z^4=10000 equation:

Simplifying
z4 = 10000

Solving
z4 = 10000

Solving for variable 'z'.

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

Simplifying
z4 = 10000

Reorder the terms:
-10000 + z4 = 10000 + -10000

Combine like terms: 10000 + -10000 = 0
-10000 + z4 = 0

Factor a difference between two squares.
(100 + z2)(-100 + z2) = 0

Factor a difference between two squares.
(100 + z2)((10 + z)(-10 + z)) = 0

Subproblem 1
Set the factor '(100 + z2)' equal to zero and attempt to solve:

Simplifying
100 + z2 = 0

Solving
100 + z2 = 0

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

Add '-100' to each side of the equation.
100 + -100 + z2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + z2 = 0 + -100
z2 = 0 + -100

Combine like terms: 0 + -100 = -100
z2 = -100

Simplifying
z2 = -100

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 '(10 + z)' equal to zero and attempt to solve:

Simplifying
10 + z = 0

Solving
10 + z = 0

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

Add '-10' to each side of the equation.
10 + -10 + z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + z = 0 + -10
z = 0 + -10

Combine like terms: 0 + -10 = -10
z = -10

Simplifying
z = -10
Subproblem 3
Set the factor '(-10 + z)' equal to zero and attempt to solve:

Simplifying
-10 + z = 0

Solving
-10 + z = 0

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

Add '10' to each side of the equation.
-10 + 10 + z = 0 + 10

Combine like terms: -10 + 10 = 0
0 + z = 0 + 10
z = 0 + 10

Combine like terms: 0 + 10 = 10
z = 10

Simplifying
z = 10
Solution
z = {-10, 10}