(-10x^4+x^8+5)=0

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Solution for (-10x^4+x^8+5)=0 equation: 


Simplifying
(-10x4 + x8 + 5) = 0

Reorder the terms:
(5 + -10x4 + x8) = 0

Remove parenthesis around (5 + -10x4 + x8)
5 + -10x4 + x8 = 0

Solving
5 + -10x4 + x8 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -10x4 + -5 + x8 = 0 + -5

Reorder the terms:
5 + -5 + -10x4 + x8 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -10x4 + x8 = 0 + -5
-10x4 + x8 = 0 + -5

Combine like terms: 0 + -5 = -5
-10x4 + x8 = -5

The x term is -10x4.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x4 + 25 + x8 = -5 + 25

Reorder the terms:
25 + -10x4 + x8 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + -10x4 + x8 = 20

Factor a perfect square on the left side:
(x4 + -5)(x4 + -5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x4 + -5) equal to 4.472135955 and -4.472135955.


Subproblem 1
x4 + -5 = 4.472135955

Simplifying
x4 + -5 = 4.472135955

Reorder the terms:
-5 + x4 = 4.472135955

Solving
-5 + x4 = 4.472135955

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x4 = 4.472135955 + 5

Combine like terms: -5 + 5 = 0
0 + x4 = 4.472135955 + 5
x4 = 4.472135955 + 5

Combine like terms: 4.472135955 + 5 = 9.472135955
x4 = 9.472135955

Simplifying
x4 = 9.472135955

Reorder the terms:
-9.472135955 + x4 = 9.472135955 + -9.472135955

Combine like terms: 9.472135955 + -9.472135955 = 0.000000000
-9.472135955 + 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 + -5 = -4.472135955

Simplifying
x4 + -5 = -4.472135955

Reorder the terms:
-5 + x4 = -4.472135955

Solving
-5 + x4 = -4.472135955

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x4 = -4.472135955 + 5

Combine like terms: -5 + 5 = 0
0 + x4 = -4.472135955 + 5
x4 = -4.472135955 + 5

Combine like terms: -4.472135955 + 5 = 0.527864045
x4 = 0.527864045

Simplifying
x4 = 0.527864045

Reorder the terms:
-0.527864045 + x4 = 0.527864045 + -0.527864045

Combine like terms: 0.527864045 + -0.527864045 = 0.000000000
-0.527864045 + 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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