n^4=10000

Solution for n^4=10000 equation:

Simplifying
n4 = 10000

Solving
n4 = 10000

Solving for variable 'n'.

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

Simplifying
n4 = 10000

Reorder the terms:
-10000 + n4 = 10000 + -10000

Combine like terms: 10000 + -10000 = 0
-10000 + n4 = 0

Factor a difference between two squares.
(100 + n2)(-100 + n2) = 0

Factor a difference between two squares.
(100 + n2)((10 + n)(-10 + n)) = 0

Subproblem 1
Set the factor '(100 + n2)' equal to zero and attempt to solve:

Simplifying
100 + n2 = 0

Solving
100 + n2 = 0

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

Add '-100' to each side of the equation.
100 + -100 + n2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + n2 = 0 + -100
n2 = 0 + -100

Combine like terms: 0 + -100 = -100
n2 = -100

Simplifying
n2 = -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 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 0

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

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

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

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

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

Simplifying
-10 + n = 0

Solving
-10 + n = 0

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

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

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

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

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