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

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


Simplifying
25x8 + -116x4 + 64 = 0

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

Solving
64 + -116x4 + 25x8 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
((4 + 5x2)(4 + -5x2))(4 + -1x4) = 0

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


Subproblem 1
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 2
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}

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

Simplifying
2 + x2 = 0

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

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

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

Simplifying
x2 = -2

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 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

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

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

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

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {-0.894427191, 0.894427191, -1.414213562, 1.414213562}

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