8*(x^4)-8*(x^2)+1=0

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Solution for 8*(x^4)-8*(x^2)+1=0 equation: 


Simplifying
8(x4) + -8(x2) + 1 = 0

Reorder the terms:
1 + -8x2 + 8x4 = 0

Solving
1 + -8x2 + 8x4 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
0.125 + -1x2 + x4 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -1x2 + -0.125 + x4 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -1x2 + x4 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -1x2 + x4 = 0 + -0.125
-1x2 + x4 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-1x2 + x4 = -0.125

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = -0.125 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = -0.125 + 0.25

Combine like terms: -0.125 + 0.25 = 0.125
0.25 + -1x2 + x4 = 0.125

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 0.353553391 and -0.353553391.


Subproblem 1
x2 + -0.5 = 0.353553391

Simplifying
x2 + -0.5 = 0.353553391

Reorder the terms:
-0.5 + x2 = 0.353553391

Solving
-0.5 + x2 = 0.353553391

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = 0.353553391 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 0.353553391 + 0.5
x2 = 0.353553391 + 0.5

Combine like terms: 0.353553391 + 0.5 = 0.853553391
x2 = 0.853553391

Simplifying
x2 = 0.853553391

Take the square root of each side:
x = {-0.923879533, 0.923879533}


Subproblem 2
x2 + -0.5 = -0.353553391

Simplifying
x2 + -0.5 = -0.353553391

Reorder the terms:
-0.5 + x2 = -0.353553391

Solving
-0.5 + x2 = -0.353553391

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = -0.353553391 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -0.353553391 + 0.5
x2 = -0.353553391 + 0.5

Combine like terms: -0.353553391 + 0.5 = 0.146446609
x2 = 0.146446609

Simplifying
x2 = 0.146446609

Take the square root of each side:
x = {-0.382683432, 0.382683432}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.923879533, 0.923879533, -0.382683432, 0.382683432}

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