25x^8-116x^4+16=0

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Solution for 25x^8-116x^4+16=0 equation: 


Simplifying
25x8 + -116x4 + 16 = 0

Reorder the terms:
16 + -116x4 + 25x8 = 0

Solving
16 + -116x4 + 25x8 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
25 the coefficient of the squared term: 

Divide each side by '25'.
0.64 + -4.64x4 + x8 = 0

Move the constant term to the right:

Add '-0.64' to each side of the equation.
0.64 + -4.64x4 + -0.64 + x8 = 0 + -0.64

Reorder the terms:
0.64 + -0.64 + -4.64x4 + x8 = 0 + -0.64

Combine like terms: 0.64 + -0.64 = 0.00
0.00 + -4.64x4 + x8 = 0 + -0.64
-4.64x4 + x8 = 0 + -0.64

Combine like terms: 0 + -0.64 = -0.64
-4.64x4 + x8 = -0.64

The x term is -4.64x4.  Take half its coefficient (-2.32).
Square it (5.3824) and add it to both sides.

Add '5.3824' to each side of the equation.
-4.64x4 + 5.3824 + x8 = -0.64 + 5.3824

Reorder the terms:
5.3824 + -4.64x4 + x8 = -0.64 + 5.3824

Combine like terms: -0.64 + 5.3824 = 4.7424
5.3824 + -4.64x4 + x8 = 4.7424

Factor a perfect square on the left side:
(x4 + -2.32)(x4 + -2.32) = 4.7424

Calculate the square root of the right side: 2.177705214

Break this problem into two subproblems by setting 
(x4 + -2.32) equal to 2.177705214 and -2.177705214.


Subproblem 1
x4 + -2.32 = 2.177705214

Simplifying
x4 + -2.32 = 2.177705214

Reorder the terms:
-2.32 + x4 = 2.177705214

Solving
-2.32 + x4 = 2.177705214

Solving for variable 'x'.

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

Add '2.32' to each side of the equation.
-2.32 + 2.32 + x4 = 2.177705214 + 2.32

Combine like terms: -2.32 + 2.32 = 0.00
0.00 + x4 = 2.177705214 + 2.32
x4 = 2.177705214 + 2.32

Combine like terms: 2.177705214 + 2.32 = 4.497705214
x4 = 4.497705214

Simplifying
x4 = 4.497705214

Reorder the terms:
-4.497705214 + x4 = 4.497705214 + -4.497705214

Combine like terms: 4.497705214 + -4.497705214 = 0.000000000
-4.497705214 + x4 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
x4 + -2.32 = -2.177705214

Simplifying
x4 + -2.32 = -2.177705214

Reorder the terms:
-2.32 + x4 = -2.177705214

Solving
-2.32 + x4 = -2.177705214

Solving for variable 'x'.

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

Add '2.32' to each side of the equation.
-2.32 + 2.32 + x4 = -2.177705214 + 2.32

Combine like terms: -2.32 + 2.32 = 0.00
0.00 + x4 = -2.177705214 + 2.32
x4 = -2.177705214 + 2.32

Combine like terms: -2.177705214 + 2.32 = 0.142294786
x4 = 0.142294786

Simplifying
x4 = 0.142294786

Reorder the terms:
-0.142294786 + x4 = 0.142294786 + -0.142294786

Combine like terms: 0.142294786 + -0.142294786 = 0.000000000
-0.142294786 + x4 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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