3x^4-4x^2-1=0

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Solution for 3x^4-4x^2-1=0 equation:


Simplifying
3x4 + -4x2 + -1 = 0

Reorder the terms:
-1 + -4x2 + 3x4 = 0

Solving
-1 + -4x2 + 3x4 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-0.3333333333 + -1.333333333x2 + x4 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -1.333333333x2 + 0.3333333333 + x4 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -1.333333333x2 + x4 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -1.333333333x2 + x4 = 0 + 0.3333333333
-1.333333333x2 + x4 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-1.333333333x2 + x4 = 0.3333333333

The x term is -1.333333333x2.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x2 + 0.4444444442 + x4 = 0.3333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x2 + x4 = 0.3333333333 + 0.4444444442

Combine like terms: 0.3333333333 + 0.4444444442 = 0.7777777775
0.4444444442 + -1.333333333x2 + x4 = 0.7777777775

Factor a perfect square on the left side:
(x2 + -0.6666666665)(x2 + -0.6666666665) = 0.7777777775

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(x2 + -0.6666666665) equal to 0.881917104 and -0.881917104.

Subproblem 1

x2 + -0.6666666665 = 0.881917104 Simplifying x2 + -0.6666666665 = 0.881917104 Reorder the terms: -0.6666666665 + x2 = 0.881917104 Solving -0.6666666665 + x2 = 0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x2 = 0.881917104 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x2 = 0.881917104 + 0.6666666665 x2 = 0.881917104 + 0.6666666665 Combine like terms: 0.881917104 + 0.6666666665 = 1.5485837705 x2 = 1.5485837705 Simplifying x2 = 1.5485837705 Take the square root of each side: x = {-1.244421058, 1.244421058}

Subproblem 2

x2 + -0.6666666665 = -0.881917104 Simplifying x2 + -0.6666666665 = -0.881917104 Reorder the terms: -0.6666666665 + x2 = -0.881917104 Solving -0.6666666665 + x2 = -0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x2 = -0.881917104 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x2 = -0.881917104 + 0.6666666665 x2 = -0.881917104 + 0.6666666665 Combine like terms: -0.881917104 + 0.6666666665 = -0.2152504375 x2 = -0.2152504375 Simplifying x2 = -0.2152504375 Reorder the terms: 0.2152504375 + x2 = -0.2152504375 + 0.2152504375 Combine like terms: -0.2152504375 + 0.2152504375 = 0.0000000000 0.2152504375 + x2 = 0.0000000000 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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