64=w^4

Solution for 64=w^4 equation:

Simplifying
64 = w4

Solving
64 = w4

Solving for variable 'w'.

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

Add '-1w4' to each side of the equation.
64 + -1w4 = w4 + -1w4

Combine like terms: w4 + -1w4 = 0
64 + -1w4 = 0

Add '-64' to each side of the equation.
64 + -64 + -1w4 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -1w4 = 0 + -64
-1w4 = 0 + -64

Combine like terms: 0 + -64 = -64
-1w4 = -64

Divide each side by '-1'.
w4 = 64

Simplifying
w4 = 64

Reorder the terms:
-64 + w4 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + w4 = 0

Factor a difference between two squares.
(8 + w2)(-8 + w2) = 0

Subproblem 1
Set the factor '(8 + w2)' equal to zero and attempt to solve:

Simplifying
8 + w2 = 0

Solving
8 + w2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + w2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w2 = 0 + -8
w2 = 0 + -8

Combine like terms: 0 + -8 = -8
w2 = -8

Simplifying
w2 = -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 + w2)' equal to zero and attempt to solve:

Simplifying
-8 + w2 = 0

Solving
-8 + w2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + w2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + w2 = 0 + 8
w2 = 0 + 8

Combine like terms: 0 + 8 = 8
w2 = 8

Simplifying
w2 = 8

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