64x^8-116x^4+25=0

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Solution for 64x^8-116x^4+25=0 equation: 


Simplifying
64x8 + -116x4 + 25 = 0

Reorder the terms:
25 + -116x4 + 64x8 = 0

Solving
25 + -116x4 + 64x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x4)(25 + -16x4) = 0

Factor a difference between two squares.
((1 + 2x2)(1 + -2x2))(25 + -16x4) = 0

Factor a difference between two squares.
((5 + 4x2)(5 + -4x2))(1 + 2x2)(1 + -2x2) = 0


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

Simplifying
1 + 2x2 = 0

Solving
1 + 2x2 = 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 + 2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x2 = 0 + -1
2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
2x2 = -1

Divide each side by '2'.
x2 = -0.5

Simplifying
x2 = -0.5

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

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 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 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 = 0 + -1
-2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 = -1

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}

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

Simplifying
5 + 4x2 = 0

Solving
5 + 4x2 = 0

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

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

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

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

Divide each side by '4'.
x2 = -1.25

Simplifying
x2 = -1.25

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

Simplifying
5 + -4x2 = 0

Solving
5 + -4x2 = 0

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

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

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

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

Divide each side by '-4'.
x2 = 1.25

Simplifying
x2 = 1.25

Take the square root of each side:
x = {-1.118033989, 1.118033989}
Solution
x = {-0.707106781, 0.707106781, -1.118033989, 1.118033989}

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