4w^4-81=

Solution for 4w^4-81= equation:

Simplifying
4w4 + -81 = 0

Reorder the terms:
-81 + 4w4 = 0

Solving
-81 + 4w4 = 0

Solving for variable 'w'.

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

Add '81' to each side of the equation.
-81 + 81 + 4w4 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 4w4 = 0 + 81
4w4 = 0 + 81

Combine like terms: 0 + 81 = 81
4w4 = 81

Divide each side by '4'.
w4 = 20.25

Simplifying
w4 = 20.25

Reorder the terms:
-20.25 + w4 = 20.25 + -20.25

Combine like terms: 20.25 + -20.25 = 0.00
-20.25 + w4 = 0.00

Factor a difference between two squares.
(4.5 + w2)(-4.5 + w2) = 0.00

Subproblem 1
Set the factor '(4.5 + w2)' equal to zero and attempt to solve:

Simplifying
4.5 + w2 = 0

Solving
4.5 + w2 = 0

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w2 = 0 + -4.5
w2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
w2 = -4.5

Simplifying
w2 = -4.5

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 '(-4.5 + w2)' equal to zero and attempt to solve:

Simplifying
-4.5 + w2 = 0

Solving
-4.5 + w2 = 0

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + w2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + w2 = 0 + 4.5
w2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
w2 = 4.5

Simplifying
w2 = 4.5

Take the square root of each side:
w = {-2.121320344, 2.121320344}
Solution
w = {-2.121320344, 2.121320344}