x^8+254x^4+1=0

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Solution for x^8+254x^4+1=0 equation: 


Simplifying
x8 + 254x4 + 1 = 0

Reorder the terms:
1 + 254x4 + x8 = 0

Solving
1 + 254x4 + x8 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 254x4 + -1 + x8 = 0 + -1

Reorder the terms:
1 + -1 + 254x4 + x8 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 254x4 + x8 = 0 + -1
254x4 + x8 = 0 + -1

Combine like terms: 0 + -1 = -1
254x4 + x8 = -1

The x term is 254x4.  Take half its coefficient (127).
Square it (16129) and add it to both sides.

Add '16129' to each side of the equation.
254x4 + 16129 + x8 = -1 + 16129

Reorder the terms:
16129 + 254x4 + x8 = -1 + 16129

Combine like terms: -1 + 16129 = 16128
16129 + 254x4 + x8 = 16128

Factor a perfect square on the left side:
(x4 + 127)(x4 + 127) = 16128

Calculate the square root of the right side: 126.996062931

Break this problem into two subproblems by setting 
(x4 + 127) equal to 126.996062931 and -126.996062931.


Subproblem 1
x4 + 127 = 126.996062931

Simplifying
x4 + 127 = 126.996062931

Reorder the terms:
127 + x4 = 126.996062931

Solving
127 + x4 = 126.996062931

Solving for variable 'x'.

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

Add '-127' to each side of the equation.
127 + -127 + x4 = 126.996062931 + -127

Combine like terms: 127 + -127 = 0
0 + x4 = 126.996062931 + -127
x4 = 126.996062931 + -127

Combine like terms: 126.996062931 + -127 = -0.003937069
x4 = -0.003937069

Simplifying
x4 = -0.003937069

Reorder the terms:
0.003937069 + x4 = -0.003937069 + 0.003937069

Combine like terms: -0.003937069 + 0.003937069 = 0.000000000
0.003937069 + 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 + 127 = -126.996062931

Simplifying
x4 + 127 = -126.996062931

Reorder the terms:
127 + x4 = -126.996062931

Solving
127 + x4 = -126.996062931

Solving for variable 'x'.

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

Add '-127' to each side of the equation.
127 + -127 + x4 = -126.996062931 + -127

Combine like terms: 127 + -127 = 0
0 + x4 = -126.996062931 + -127
x4 = -126.996062931 + -127

Combine like terms: -126.996062931 + -127 = -253.996062931
x4 = -253.996062931

Simplifying
x4 = -253.996062931

Reorder the terms:
253.996062931 + x4 = -253.996062931 + 253.996062931

Combine like terms: -253.996062931 + 253.996062931 = 0.000000000
253.996062931 + 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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