s^4-1=

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Solution for s^4-1= equation:


Simplifying
s4 + -1 = 0

Reorder the terms:
-1 + s4 = 0

Solving
-1 + s4 = 0

Solving for variable 's'.

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

Add '1' to each side of the equation.
-1 + 1 + s4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + s4 = 0 + 1
s4 = 0 + 1

Combine like terms: 0 + 1 = 1
s4 = 1

Simplifying
s4 = 1

Reorder the terms:
-1 + s4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + s4 = 0

Factor a difference between two squares.
(1 + s2)(-1 + s2) = 0

Factor a difference between two squares.
(1 + s2)((1 + s)(-1 + s)) = 0

Subproblem 1

Set the factor '(1 + s2)' equal to zero and attempt to solve: Simplifying 1 + s2 = 0 Solving 1 + s2 = 0 Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + s2 = 0 + -1 s2 = 0 + -1 Combine like terms: 0 + -1 = -1 s2 = -1 Simplifying s2 = -1 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 + s)' equal to zero and attempt to solve: Simplifying 1 + s = 0 Solving 1 + s = 0 Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + s = 0 + -1 s = 0 + -1 Combine like terms: 0 + -1 = -1 s = -1 Simplifying s = -1

Subproblem 3

Set the factor '(-1 + s)' equal to zero and attempt to solve: Simplifying -1 + s = 0 Solving -1 + s = 0 Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = 0 + 1 Combine like terms: -1 + 1 = 0 0 + s = 0 + 1 s = 0 + 1 Combine like terms: 0 + 1 = 1 s = 1 Simplifying s = 1

Solution

s = {-1, 1}

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