r^4-2401=0

Solution for r^4-2401=0 equation:

Simplifying
r4 + -2401 = 0

Reorder the terms:
-2401 + r4 = 0

Solving
-2401 + r4 = 0

Solving for variable 'r'.

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

Add '2401' to each side of the equation.
-2401 + 2401 + r4 = 0 + 2401

Combine like terms: -2401 + 2401 = 0
0 + r4 = 0 + 2401
r4 = 0 + 2401

Combine like terms: 0 + 2401 = 2401
r4 = 2401

Simplifying
r4 = 2401

Reorder the terms:
-2401 + r4 = 2401 + -2401

Combine like terms: 2401 + -2401 = 0
-2401 + r4 = 0

Factor a difference between two squares.
(49 + r2)(-49 + r2) = 0

Factor a difference between two squares.
(49 + r2)((7 + r)(-7 + r)) = 0

Subproblem 1
Set the factor '(49 + r2)' equal to zero and attempt to solve:

Simplifying
49 + r2 = 0

Solving
49 + r2 = 0

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

Add '-49' to each side of the equation.
49 + -49 + r2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + r2 = 0 + -49
r2 = 0 + -49

Combine like terms: 0 + -49 = -49
r2 = -49

Simplifying
r2 = -49

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 '(7 + r)' equal to zero and attempt to solve:

Simplifying
7 + r = 0

Solving
7 + r = 0

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

Add '-7' to each side of the equation.
7 + -7 + r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + r = 0 + -7
r = 0 + -7

Combine like terms: 0 + -7 = -7
r = -7

Simplifying
r = -7
Subproblem 3
Set the factor '(-7 + r)' equal to zero and attempt to solve:

Simplifying
-7 + r = 0

Solving
-7 + r = 0

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

Add '7' to each side of the equation.
-7 + 7 + r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + r = 0 + 7
r = 0 + 7

Combine like terms: 0 + 7 = 7
r = 7

Simplifying
r = 7
Solution
r = {-7, 7}