r^4+r^2-2=0

Solution for r^4+r^2-2=0 equation:

Simplifying
r4 + r2 + -2 = 0

Reorder the terms:
-2 + r2 + r4 = 0

Solving
-2 + r2 + r4 = 0

Solving for variable 'r'.

Factor a trinomial.
(-2 + -1r2)(1 + -1r2) = 0

Factor a difference between two squares.
(-2 + -1r2)((1 + r)(1 + -1r)) = 0

Subproblem 1
Set the factor '(-2 + -1r2)' equal to zero and attempt to solve:

Simplifying
-2 + -1r2 = 0

Solving
-2 + -1r2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r2 = 0 + 2
-1r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1r2 = 2

Divide each side by '-1'.
r2 = -2

Simplifying
r2 = -2

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 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 0

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

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

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

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

Simplifying
r = -1
Subproblem 3
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {-1, 1}