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

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


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

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

Solving
-1 + x2 + (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 + 0.125x2 + x4 = 0

Move the constant term to the right:

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

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

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

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

The x term is x2.  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.
0.125x2 + 0.25 + x4 = 0.125 + 0.25

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

Combine like terms: 0.125 + 0.25 = 0.375
0.25 + 0.125x2 + x4 = 0.375

Factor a perfect square on the left side:
((x2) + 0.5)((x2) + 0.5) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
((x2) + 0.5) equal to 0.612372436 and -0.612372436.


Subproblem 1
(x2) + 0.5 = 0.612372436

Simplifying
(x2) + 0.5 = 0.612372436
x2 + 0.5 = 0.612372436

Reorder the terms:
0.5 + x2 = 0.612372436

Solving
0.5 + x2 = 0.612372436

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 = 0.612372436 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 0.612372436 + -0.5
x2 = 0.612372436 + -0.5

Combine like terms: 0.612372436 + -0.5 = 0.112372436
x2 = 0.112372436

Simplifying
x2 = 0.112372436

Take the square root of each side:
x = {-0.335219982, 0.335219982}


Subproblem 2
(x2) + 0.5 = -0.612372436

Simplifying
(x2) + 0.5 = -0.612372436
x2 + 0.5 = -0.612372436

Reorder the terms:
0.5 + x2 = -0.612372436

Solving
0.5 + x2 = -0.612372436

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 = -0.612372436 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -0.612372436 + -0.5
x2 = -0.612372436 + -0.5

Combine like terms: -0.612372436 + -0.5 = -1.112372436
x2 = -1.112372436

Simplifying
x2 = -1.112372436

Reorder the terms:
1.112372436 + x2 = -1.112372436 + 1.112372436

Combine like terms: -1.112372436 + 1.112372436 = 0.000000000
1.112372436 + x2 = 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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