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

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


Simplifying
3x4 + 2x2 + -4 = 0

Reorder the terms:
-4 + 2x2 + 3x4 = 0

Solving
-4 + 2x2 + 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'.
-1.333333333 + 0.6666666667x2 + x4 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 0.6666666667x2 + 1.333333333 + x4 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 0.6666666667x2 + x4 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 0.6666666667x2 + x4 = 0 + 1.333333333
0.6666666667x2 + x4 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
0.6666666667x2 + x4 = 1.333333333

The x term is 0.6666666667x2.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x2 + 0.1111111112 + x4 = 1.333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x2 + x4 = 1.333333333 + 0.1111111112

Combine like terms: 1.333333333 + 0.1111111112 = 1.4444444442
0.1111111112 + 0.6666666667x2 + x4 = 1.4444444442

Factor a perfect square on the left side:
(x2 + 0.3333333334)(x2 + 0.3333333334) = 1.4444444442

Calculate the square root of the right side: 1.201850425

Break this problem into two subproblems by setting 
(x2 + 0.3333333334) equal to 1.201850425 and -1.201850425.

Subproblem 1

x2 + 0.3333333334 = 1.201850425 Simplifying x2 + 0.3333333334 = 1.201850425 Reorder the terms: 0.3333333334 + x2 = 1.201850425 Solving 0.3333333334 + x2 = 1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x2 = 1.201850425 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x2 = 1.201850425 + -0.3333333334 x2 = 1.201850425 + -0.3333333334 Combine like terms: 1.201850425 + -0.3333333334 = 0.8685170916 x2 = 0.8685170916 Simplifying x2 = 0.8685170916 Take the square root of each side: x = {-0.931942644, 0.931942644}

Subproblem 2

x2 + 0.3333333334 = -1.201850425 Simplifying x2 + 0.3333333334 = -1.201850425 Reorder the terms: 0.3333333334 + x2 = -1.201850425 Solving 0.3333333334 + x2 = -1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x2 = -1.201850425 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x2 = -1.201850425 + -0.3333333334 x2 = -1.201850425 + -0.3333333334 Combine like terms: -1.201850425 + -0.3333333334 = -1.5351837584 x2 = -1.5351837584 Simplifying x2 = -1.5351837584 Reorder the terms: 1.5351837584 + x2 = -1.5351837584 + 1.5351837584 Combine like terms: -1.5351837584 + 1.5351837584 = 0.0000000000 1.5351837584 + 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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