x^4-0.4x^2-0.04123=0

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Solution for x^4-0.4x^2-0.04123=0 equation: 


Simplifying
x4 + -0.4x2 + -0.04123 = 0

Reorder the terms:
-0.04123 + -0.4x2 + x4 = 0

Solving
-0.04123 + -0.4x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.04123' to each side of the equation.
-0.04123 + -0.4x2 + 0.04123 + x4 = 0 + 0.04123

Reorder the terms:
-0.04123 + 0.04123 + -0.4x2 + x4 = 0 + 0.04123

Combine like terms: -0.04123 + 0.04123 = 0.00000
0.00000 + -0.4x2 + x4 = 0 + 0.04123
-0.4x2 + x4 = 0 + 0.04123

Combine like terms: 0 + 0.04123 = 0.04123
-0.4x2 + x4 = 0.04123

The x term is -0.4x2.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x2 + 0.04 + x4 = 0.04123 + 0.04

Reorder the terms:
0.04 + -0.4x2 + x4 = 0.04123 + 0.04

Combine like terms: 0.04123 + 0.04 = 0.08123
0.04 + -0.4x2 + x4 = 0.08123

Factor a perfect square on the left side:
(x2 + -0.2)(x2 + -0.2) = 0.08123

Calculate the square root of the right side: 0.285008772

Break this problem into two subproblems by setting 
(x2 + -0.2) equal to 0.285008772 and -0.285008772.


Subproblem 1
x2 + -0.2 = 0.285008772

Simplifying
x2 + -0.2 = 0.285008772

Reorder the terms:
-0.2 + x2 = 0.285008772

Solving
-0.2 + x2 = 0.285008772

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x2 = 0.285008772 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x2 = 0.285008772 + 0.2
x2 = 0.285008772 + 0.2

Combine like terms: 0.285008772 + 0.2 = 0.485008772
x2 = 0.485008772

Simplifying
x2 = 0.485008772

Take the square root of each side:
x = {-0.696425712, 0.696425712}


Subproblem 2
x2 + -0.2 = -0.285008772

Simplifying
x2 + -0.2 = -0.285008772

Reorder the terms:
-0.2 + x2 = -0.285008772

Solving
-0.2 + x2 = -0.285008772

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x2 = -0.285008772 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x2 = -0.285008772 + 0.2
x2 = -0.285008772 + 0.2

Combine like terms: -0.285008772 + 0.2 = -0.085008772
x2 = -0.085008772

Simplifying
x2 = -0.085008772

Reorder the terms:
0.085008772 + x2 = -0.085008772 + 0.085008772

Combine like terms: -0.085008772 + 0.085008772 = 0.000000000
0.085008772 + 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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