4x^4-x^2-1=0

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Solution for 4x^4-x^2-1=0 equation: 


Simplifying
4x4 + -1x2 + -1 = 0

Reorder the terms:
-1 + -1x2 + 4x4 = 0

Solving
-1 + -1x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-0.25 + -0.25x2 + x4 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.25x2 + 0.25 + x4 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.25x2 + x4 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.25x2 + x4 = 0 + 0.25
-0.25x2 + x4 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.25x2 + x4 = 0.25

The x term is -0.25x2.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x2 + 0.015625 + x4 = 0.25 + 0.015625

Reorder the terms:
0.015625 + -0.25x2 + x4 = 0.25 + 0.015625

Combine like terms: 0.25 + 0.015625 = 0.265625
0.015625 + -0.25x2 + x4 = 0.265625

Factor a perfect square on the left side:
(x2 + -0.125)(x2 + -0.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x2 + -0.125) equal to 0.515388203 and -0.515388203.


Subproblem 1
x2 + -0.125 = 0.515388203

Simplifying
x2 + -0.125 = 0.515388203

Reorder the terms:
-0.125 + x2 = 0.515388203

Solving
-0.125 + x2 = 0.515388203

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x2 = 0.515388203 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x2 = 0.515388203 + 0.125
x2 = 0.515388203 + 0.125

Combine like terms: 0.515388203 + 0.125 = 0.640388203
x2 = 0.640388203

Simplifying
x2 = 0.640388203

Take the square root of each side:
x = {-0.80024259, 0.80024259}


Subproblem 2
x2 + -0.125 = -0.515388203

Simplifying
x2 + -0.125 = -0.515388203

Reorder the terms:
-0.125 + x2 = -0.515388203

Solving
-0.125 + x2 = -0.515388203

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x2 = -0.515388203 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x2 = -0.515388203 + 0.125
x2 = -0.515388203 + 0.125

Combine like terms: -0.515388203 + 0.125 = -0.390388203
x2 = -0.390388203

Simplifying
x2 = -0.390388203

Reorder the terms:
0.390388203 + x2 = -0.390388203 + 0.390388203

Combine like terms: -0.390388203 + 0.390388203 = 0.000000000
0.390388203 + 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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