v^4-64=0

Solution for v^4-64=0 equation:

Simplifying
v4 + -64 = 0

Reorder the terms:
-64 + v4 = 0

Solving
-64 + v4 = 0

Solving for variable 'v'.

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

Add '64' to each side of the equation.
-64 + 64 + v4 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + v4 = 0 + 64
v4 = 0 + 64

Combine like terms: 0 + 64 = 64
v4 = 64

Simplifying
v4 = 64

Reorder the terms:
-64 + v4 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + v4 = 0

Factor a difference between two squares.
(8 + v2)(-8 + v2) = 0

Subproblem 1
Set the factor '(8 + v2)' equal to zero and attempt to solve:

Simplifying
8 + v2 = 0

Solving
8 + v2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + v2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + v2 = 0 + -8
v2 = 0 + -8

Combine like terms: 0 + -8 = -8
v2 = -8

Simplifying
v2 = -8

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 '(-8 + v2)' equal to zero and attempt to solve:

Simplifying
-8 + v2 = 0

Solving
-8 + v2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + v2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + v2 = 0 + 8
v2 = 0 + 8

Combine like terms: 0 + 8 = 8
v2 = 8

Simplifying
v2 = 8

Take the square root of each side:
v = {-2.828427125, 2.828427125}
Solution
v = {-2.828427125, 2.828427125}