x^4-x^2=0.0084

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Solution for x^4-x^2=0.0084 equation: 


Simplifying
x4 + -1x2 = 0.0084

Reorder the terms:
-1x2 + x4 = 0.0084

Solving
-1x2 + x4 = 0.0084

Solving for variable 'x'.

Reorder the terms:
-0.0084 + -1x2 + x4 = 0.0084 + -0.0084

Combine like terms: 0.0084 + -0.0084 = 0.0000
-0.0084 + -1x2 + x4 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '0.0084' to each side of the equation.
-0.0084 + -1x2 + 0.0084 + x4 = 0.0000 + 0.0084

Reorder the terms:
-0.0084 + 0.0084 + -1x2 + x4 = 0.0000 + 0.0084

Combine like terms: -0.0084 + 0.0084 = 0.0000
0.0000 + -1x2 + x4 = 0.0000 + 0.0084
-1x2 + x4 = 0.0000 + 0.0084

Combine like terms: 0.0000 + 0.0084 = 0.0084
-1x2 + x4 = 0.0084

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 = 0.0084 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 0.0084 + 0.25

Combine like terms: 0.0084 + 0.25 = 0.2584
0.25 + -1x2 + x4 = 0.2584

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 0.2584

Calculate the square root of the right side: 0.508330601

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 0.508330601 and -0.508330601.


Subproblem 1
x2 + -0.5 = 0.508330601

Simplifying
x2 + -0.5 = 0.508330601

Reorder the terms:
-0.5 + x2 = 0.508330601

Solving
-0.5 + x2 = 0.508330601

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 = 0.508330601 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 0.508330601 + 0.5
x2 = 0.508330601 + 0.5

Combine like terms: 0.508330601 + 0.5 = 1.008330601
x2 = 1.008330601

Simplifying
x2 = 1.008330601

Take the square root of each side:
x = {-1.004156662, 1.004156662}


Subproblem 2
x2 + -0.5 = -0.508330601

Simplifying
x2 + -0.5 = -0.508330601

Reorder the terms:
-0.5 + x2 = -0.508330601

Solving
-0.5 + x2 = -0.508330601

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 = -0.508330601 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -0.508330601 + 0.5
x2 = -0.508330601 + 0.5

Combine like terms: -0.508330601 + 0.5 = -0.008330601
x2 = -0.008330601

Simplifying
x2 = -0.008330601

Reorder the terms:
0.008330601 + x2 = -0.008330601 + 0.008330601

Combine like terms: -0.008330601 + 0.008330601 = 0.000000000
0.008330601 + 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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