8s^4-72=0

Solution for 8s^4-72=0 equation:

Simplifying
8s4 + -72 = 0

Reorder the terms:
-72 + 8s4 = 0

Solving
-72 + 8s4 = 0

Solving for variable 's'.

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

Add '72' to each side of the equation.
-72 + 72 + 8s4 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 8s4 = 0 + 72
8s4 = 0 + 72

Combine like terms: 0 + 72 = 72
8s4 = 72

Divide each side by '8'.
s4 = 9

Simplifying
s4 = 9

Reorder the terms:
-9 + s4 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + s4 = 0

Factor a difference between two squares.
(3 + s2)(-3 + s2) = 0

Subproblem 1
Set the factor '(3 + s2)' equal to zero and attempt to solve:

Simplifying
3 + s2 = 0

Solving
3 + s2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + s2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + s2 = 0 + -3
s2 = 0 + -3

Combine like terms: 0 + -3 = -3
s2 = -3

Simplifying
s2 = -3

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 '(-3 + s2)' equal to zero and attempt to solve:

Simplifying
-3 + s2 = 0

Solving
-3 + s2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + s2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + s2 = 0 + 3
s2 = 0 + 3

Combine like terms: 0 + 3 = 3
s2 = 3

Simplifying
s2 = 3

Take the square root of each side:
s = {-1.732050808, 1.732050808}
Solution
s = {-1.732050808, 1.732050808}