225x^8-169x^4+16=0

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Solution for 225x^8-169x^4+16=0 equation: 


Simplifying
225x8 + -169x4 + 16 = 0

Reorder the terms:
16 + -169x4 + 225x8 = 0

Solving
16 + -169x4 + 225x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -9x4)(16 + -25x4) = 0

Factor a difference between two squares.
((1 + 3x2)(1 + -3x2))(16 + -25x4) = 0

Factor a difference between two squares.
((4 + 5x2)(4 + -5x2))(1 + 3x2)(1 + -3x2) = 0


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

Simplifying
1 + 3x2 = 0

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

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

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

Divide each side by '3'.
x2 = -0.3333333333

Simplifying
x2 = -0.3333333333

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

Simplifying
1 + -3x2 = 0

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

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

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

Divide each side by '-3'.
x2 = 0.3333333333

Simplifying
x2 = 0.3333333333

Take the square root of each side:
x = {-0.577350269, 0.577350269}

Subproblem 3
Set the factor '(4 + 5x2)' equal to zero and attempt to solve:

Simplifying
4 + 5x2 = 0

Solving
4 + 5x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x2 = 0 + -4
5x2 = 0 + -4

Combine like terms: 0 + -4 = -4
5x2 = -4

Divide each side by '5'.
x2 = -0.8

Simplifying
x2 = -0.8

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 '(4 + -5x2)' equal to zero and attempt to solve:

Simplifying
4 + -5x2 = 0

Solving
4 + -5x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x2 = 0 + -4
-5x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5x2 = -4

Divide each side by '-5'.
x2 = 0.8

Simplifying
x2 = 0.8

Take the square root of each side:
x = {-0.894427191, 0.894427191}
Solution
x = {-0.577350269, 0.577350269, -0.894427191, 0.894427191}

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