4x^8-13x^4+9=0

Solution for 4x^8-13x^4+9=0 equation:

Simplifying
4x8 + -13x4 + 9 = 0

Reorder the terms:
9 + -13x4 + 4x8 = 0

Solving
9 + -13x4 + 4x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x4)(9 + -4x4) = 0

Factor a difference between two squares.
((1 + x2)(1 + -1x2))(9 + -4x4) = 0

Factor a difference between two squares.
((1 + x2)((1 + x)(1 + -1x)))(9 + -4x4) = 0

Factor a difference between two squares.
((3 + 2x2)(3 + -2x2))(1 + x2)(1 + x)(1 + -1x) = 0

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

Simplifying
1 + x2 = 0

Solving
1 + x2 = 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 + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -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 + 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 3
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 4
Set the factor '(3 + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + 2x2 = 0

Solving
3 + 2x2 = 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 + 2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x2 = 0 + -3
2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
2x2 = -3

Divide each side by '2'.
x2 = -1.5

Simplifying
x2 = -1.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 5
Set the factor '(3 + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x2 = 0

Solving
3 + -2x2 = 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 + -2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x2 = 0 + -3
-2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x2 = -3

Divide each side by '-2'.
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {-1, 1, -1.224744871, 1.224744871}