Simplifying
x^{4} + -10x^{2} + 9 = 0
Reorder the terms:
9 + -10x^{2} + x^{4} = 0
Solving
9 + -10x^{2} + x^{4} = 0
Solving for variable 'x'.
Factor a trinomial.
(1 + -1x^{2})(9 + -1x^{2}) = 0
Factor a difference between two squares.
((1 + x)(1 + -1x))(9 + -1x^{2}) = 0
Factor a difference between two squares.
((3 + x)(3 + -1x))(1 + x)(1 + -1x) = 0
#### Subproblem 1

Set the factor '(1 + x)' equal to zero and attempt to solve:
Simplifying
1 + x = 0
Solving
1 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1
Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1
Combine like terms: 0 + -1 = -1
x = -1
Simplifying
x = -1
#### Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve:
Simplifying
1 + -1x = 0
Solving
1 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1
Combine like terms: 0 + -1 = -1
-1x = -1
Divide each side by '-1'.
x = 1
Simplifying
x = 1
#### Subproblem 3

Set the factor '(3 + x)' equal to zero and attempt to solve:
Simplifying
3 + x = 0
Solving
3 + x = 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 + x = 0 + -3
Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3
Combine like terms: 0 + -3 = -3
x = -3
Simplifying
x = -3
#### Subproblem 4

Set the factor '(3 + -1x)' equal to zero and attempt to solve:
Simplifying
3 + -1x = 0
Solving
3 + -1x = 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 + -1x = 0 + -3
Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3
Combine like terms: 0 + -3 = -3
-1x = -3
Divide each side by '-1'.
x = 3
Simplifying
x = 3#### Solution

x = {-1, 1, -3, 3}