r^4-9=0

Solution for r^4-9=0 equation:

Simplifying
r4 + -9 = 0

Reorder the terms:
-9 + r4 = 0

Solving
-9 + r4 = 0

Solving for variable 'r'.

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

Add '9' to each side of the equation.
-9 + 9 + r4 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + r4 = 0 + 9
r4 = 0 + 9

Combine like terms: 0 + 9 = 9
r4 = 9

Simplifying
r4 = 9

Reorder the terms:
-9 + r4 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + r4 = 0

Factor a difference between two squares.
(3 + r2)(-3 + r2) = 0

Subproblem 1
Set the factor '(3 + r2)' equal to zero and attempt to solve:

Simplifying
3 + r2 = 0

Solving
3 + r2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + r2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r2 = 0 + -3
r2 = 0 + -3

Combine like terms: 0 + -3 = -3
r2 = -3

Simplifying
r2 = -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 + r2)' equal to zero and attempt to solve:

Simplifying
-3 + r2 = 0

Solving
-3 + r2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + r2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + r2 = 0 + 3
r2 = 0 + 3

Combine like terms: 0 + 3 = 3
r2 = 3

Simplifying
r2 = 3

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