256x^8-160x^4+9=0

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Solution for 256x^8-160x^4+9=0 equation: 


Simplifying
256x8 + -160x4 + 9 = 0

Reorder the terms:
9 + -160x4 + 256x8 = 0

Solving
9 + -160x4 + 256x8 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
((1 + 4x2)(1 + -4x2))(9 + -16x4) = 0

Factor a difference between two squares.
((1 + 4x2)((1 + 2x)(1 + -2x)))(9 + -16x4) = 0

Factor a difference between two squares.
((3 + 4x2)(3 + -4x2))(1 + 4x2)(1 + 2x)(1 + -2x) = 0


Subproblem 1
Set the factor '(1 + 4x2)' equal to zero and attempt to solve:

Simplifying
1 + 4x2 = 0

Solving
1 + 4x2 = 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 + 4x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x2 = 0 + -1
4x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4x2 = -1

Divide each side by '4'.
x2 = -0.25

Simplifying
x2 = -0.25

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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
3 + 4x2 = 0

Solving
3 + 4x2 = 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 + 4x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x2 = 0 + -3
4x2 = 0 + -3

Combine like terms: 0 + -3 = -3
4x2 = -3

Divide each side by '4'.
x2 = -0.75

Simplifying
x2 = -0.75

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

Simplifying
3 + -4x2 = 0

Solving
3 + -4x2 = 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 + -4x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x2 = 0 + -3
-4x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4x2 = -3

Divide each side by '-4'.
x2 = 0.75

Simplifying
x2 = 0.75

Take the square root of each side:
x = {-0.866025404, 0.866025404}
Solution
x = {-0.5, 0.5, -0.866025404, 0.866025404}

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