225x^8-181x^4+36=0

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Solution for 225x^8-181x^4+36=0 equation: 


Simplifying
225x8 + -181x4 + 36 = 0

Reorder the terms:
36 + -181x4 + 225x8 = 0

Solving
36 + -181x4 + 225x8 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
((3 + 5x2)(3 + -5x2))(4 + -9x4) = 0

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


Subproblem 1
Set the factor '(3 + 5x2)' equal to zero and attempt to solve:

Simplifying
3 + 5x2 = 0

Solving
3 + 5x2 = 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 + 5x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x2 = 0 + -3
5x2 = 0 + -3

Combine like terms: 0 + -3 = -3
5x2 = -3

Divide each side by '5'.
x2 = -0.6

Simplifying
x2 = -0.6

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

Simplifying
3 + -5x2 = 0

Solving
3 + -5x2 = 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 + -5x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x2 = 0 + -3
-5x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5x2 = -3

Divide each side by '-5'.
x2 = 0.6

Simplifying
x2 = 0.6

Take the square root of each side:
x = {-0.774596669, 0.774596669}

Subproblem 3
Set the factor '(2 + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + 3x2 = 0

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

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

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

Divide each side by '3'.
x2 = -0.6666666667

Simplifying
x2 = -0.6666666667

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 '(2 + -3x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x2 = 0

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

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

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

Divide each side by '-3'.
x2 = 0.6666666667

Simplifying
x2 = 0.6666666667

Take the square root of each side:
x = {-0.816496581, 0.816496581}
Solution
x = {-0.774596669, 0.774596669, -0.816496581, 0.816496581}

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