0=x^4-9

Solution for 0=x^4-9 equation:

Simplifying
0 = x4 + -9

Reorder the terms:
0 = -9 + x4

Solving
0 = -9 + x4

Solving for variable 'x'.

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

Add '-1x4' to each side of the equation.
0 + -1x4 = -9 + x4 + -1x4
Remove the zero:
-1x4 = -9 + x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-1x4 = -9 + 0
-1x4 = -9

Divide each side by '-1'.
x4 = 9

Simplifying
x4 = 9

Reorder the terms:
-9 + x4 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + x4 = 0

Factor a difference between two squares.
(3 + x2)(-3 + x2) = 0

Subproblem 1
Set the factor '(3 + x2)' equal to zero and attempt to solve:

Simplifying
3 + x2 = 0

Solving
3 + x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x2 = 0 + -3
x2 = 0 + -3

Combine like terms: 0 + -3 = -3
x2 = -3

Simplifying
x2 = -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 + x2)' equal to zero and attempt to solve:

Simplifying
-3 + x2 = 0

Solving
-3 + x2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x2 = 0 + 3
x2 = 0 + 3

Combine like terms: 0 + 3 = 3
x2 = 3

Simplifying
x2 = 3

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