x^4-0.4x^2-0.2345=0

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Solution for x^4-0.4x^2-0.2345=0 equation: 


Simplifying
x4 + -0.4x2 + -0.2345 = 0

Reorder the terms:
-0.2345 + -0.4x2 + x4 = 0

Solving
-0.2345 + -0.4x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.2345' to each side of the equation.
-0.2345 + -0.4x2 + 0.2345 + x4 = 0 + 0.2345

Reorder the terms:
-0.2345 + 0.2345 + -0.4x2 + x4 = 0 + 0.2345

Combine like terms: -0.2345 + 0.2345 = 0.0000
0.0000 + -0.4x2 + x4 = 0 + 0.2345
-0.4x2 + x4 = 0 + 0.2345

Combine like terms: 0 + 0.2345 = 0.2345
-0.4x2 + x4 = 0.2345

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 = 0.2345 + 0.04

Reorder the terms:
0.04 + -0.4x2 + x4 = 0.2345 + 0.04

Combine like terms: 0.2345 + 0.04 = 0.2745
0.04 + -0.4x2 + x4 = 0.2745

Factor a perfect square on the left side:
(x2 + -0.2)(x2 + -0.2) = 0.2745

Calculate the square root of the right side: 0.523927476

Break this problem into two subproblems by setting 
(x2 + -0.2) equal to 0.523927476 and -0.523927476.


Subproblem 1
x2 + -0.2 = 0.523927476

Simplifying
x2 + -0.2 = 0.523927476

Reorder the terms:
-0.2 + x2 = 0.523927476

Solving
-0.2 + x2 = 0.523927476

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 = 0.523927476 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x2 = 0.523927476 + 0.2
x2 = 0.523927476 + 0.2

Combine like terms: 0.523927476 + 0.2 = 0.723927476
x2 = 0.723927476

Simplifying
x2 = 0.723927476

Take the square root of each side:
x = {-0.850839277, 0.850839277}


Subproblem 2
x2 + -0.2 = -0.523927476

Simplifying
x2 + -0.2 = -0.523927476

Reorder the terms:
-0.2 + x2 = -0.523927476

Solving
-0.2 + x2 = -0.523927476

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 = -0.523927476 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x2 = -0.523927476 + 0.2
x2 = -0.523927476 + 0.2

Combine like terms: -0.523927476 + 0.2 = -0.323927476
x2 = -0.323927476

Simplifying
x2 = -0.323927476

Reorder the terms:
0.323927476 + x2 = -0.323927476 + 0.323927476

Combine like terms: -0.323927476 + 0.323927476 = 0.000000000
0.323927476 + 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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