x^4-4x^2=3

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


Simplifying
x4 + -4x2 = 3

Reorder the terms:
-4x2 + x4 = 3

Solving
-4x2 + x4 = 3

Solving for variable 'x'.

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

Combine like terms: 3 + -3 = 0
-3 + -4x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4x2 + 3 + x4 = 0 + 3

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

Combine like terms: -3 + 3 = 0
0 + -4x2 + x4 = 0 + 3
-4x2 + x4 = 0 + 3

Combine like terms: 0 + 3 = 3
-4x2 + x4 = 3

The x term is -4x2.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x2 + 4 + x4 = 3 + 4

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

Combine like terms: 3 + 4 = 7
4 + -4x2 + x4 = 7

Factor a perfect square on the left side:
(x2 + -2)(x2 + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x2 + -2) equal to 2.645751311 and -2.645751311.

Subproblem 1

x2 + -2 = 2.645751311 Simplifying x2 + -2 = 2.645751311 Reorder the terms: -2 + x2 = 2.645751311 Solving -2 + x2 = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.645751311 + 2 x2 = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 x2 = 4.645751311 Simplifying x2 = 4.645751311 Take the square root of each side: x = {-2.155400499, 2.155400499}

Subproblem 2

x2 + -2 = -2.645751311 Simplifying x2 + -2 = -2.645751311 Reorder the terms: -2 + x2 = -2.645751311 Solving -2 + x2 = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.645751311 + 2 x2 = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 x2 = -0.645751311 Simplifying x2 = -0.645751311 Reorder the terms: 0.645751311 + x2 = -0.645751311 + 0.645751311 Combine like terms: -0.645751311 + 0.645751311 = 0.000000000 0.645751311 + 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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