25x^8-229x^4+36=0

Solution for 25x^8-229x^4+36=0 equation:

Simplifying
25x8 + -229x4 + 36 = 0

Reorder the terms:
36 + -229x4 + 25x8 = 0

Solving
36 + -229x4 + 25x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -25x4)(9 + -1x4) = 0

Factor a difference between two squares.
((2 + 5x2)(2 + -5x2))(9 + -1x4) = 0

Factor a difference between two squares.
((3 + x2)(3 + -1x2))(2 + 5x2)(2 + -5x2) = 0

Subproblem 1
Set the factor '(2 + 5x2)' equal to zero and attempt to solve:

Simplifying
2 + 5x2 = 0

Solving
2 + 5x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x2 = 0 + -2
5x2 = 0 + -2

Combine like terms: 0 + -2 = -2
5x2 = -2

Divide each side by '5'.
x2 = -0.4

Simplifying
x2 = -0.4

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 '(2 + -5x2)' equal to zero and attempt to solve:

Simplifying
2 + -5x2 = 0

Solving
2 + -5x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x2 = 0 + -2
-5x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5x2 = -2

Divide each side by '-5'.
x2 = 0.4

Simplifying
x2 = 0.4

Take the square root of each side:
x = {-0.632455532, 0.632455532}
Subproblem 3
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 4
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-0.632455532, 0.632455532, -1.732050808, 1.732050808}