16x^8-81=0

Solution for 16x^8-81=0 equation:

Simplifying
16x8 + -81 = 0

Reorder the terms:
-81 + 16x8 = 0

Solving
-81 + 16x8 = 0

Solving for variable 'x'.

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

Add '81' to each side of the equation.
-81 + 81 + 16x8 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 16x8 = 0 + 81
16x8 = 0 + 81

Combine like terms: 0 + 81 = 81
16x8 = 81

Divide each side by '16'.
x8 = 5.0625

Simplifying
x8 = 5.0625

Reorder the terms:
-5.0625 + x8 = 5.0625 + -5.0625

Combine like terms: 5.0625 + -5.0625 = 0.0000
-5.0625 + x8 = 0.0000

Factor a difference between two squares.
(2.25 + x4)(-2.25 + x4) = 0.0000

Factor a difference between two squares.
(2.25 + x4)((1.5 + x2)(-1.5 + x2)) = 0.0000

Subproblem 1
Set the factor '(2.25 + x4)' equal to zero and attempt to solve:

Simplifying
2.25 + x4 = 0

Solving
2.25 + x4 = 0

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x4 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x4 = 0 + -2.25
x4 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
x4 = -2.25

Simplifying
x4 = -2.25

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 '(1.5 + x2)' equal to zero and attempt to solve:

Simplifying
1.5 + x2 = 0

Solving
1.5 + x2 = 0

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x2 = 0 + -1.5
x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
x2 = -1.5

Simplifying
x2 = -1.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(-1.5 + x2)' equal to zero and attempt to solve:

Simplifying
-1.5 + x2 = 0

Solving
-1.5 + x2 = 0

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x2 = 0 + 1.5
x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {-1.224744871, 1.224744871}