x^4+4x^2=1

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Solution for x^4+4x^2=1 equation:


Simplifying
x4 + 4x2 = 1

Reorder the terms:
4x2 + x4 = 1

Solving
4x2 + x4 = 1

Solving for variable 'x'.

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

Combine like terms: 1 + -1 = 0
-1 + 4x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4x2 + 1 + x4 = 0 + 1

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

Combine like terms: -1 + 1 = 0
0 + 4x2 + x4 = 0 + 1
4x2 + x4 = 0 + 1

Combine like terms: 0 + 1 = 1
4x2 + x4 = 1

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 = 1 + 4

Reorder the terms:
4 + 4x2 + x4 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + 4x2 + x4 = 5

Factor a perfect square on the left side:
(x2 + 2)(x2 + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x2 + 2) equal to 2.236067978 and -2.236067978.

Subproblem 1

x2 + 2 = 2.236067978 Simplifying x2 + 2 = 2.236067978 Reorder the terms: 2 + x2 = 2.236067978 Solving 2 + x2 = 2.236067978 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 = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 2.236067978 + -2 x2 = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 x2 = 0.236067978 Simplifying x2 = 0.236067978 Take the square root of each side: x = {-0.485868272, 0.485868272}

Subproblem 2

x2 + 2 = -2.236067978 Simplifying x2 + 2 = -2.236067978 Reorder the terms: 2 + x2 = -2.236067978 Solving 2 + x2 = -2.236067978 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 = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -2.236067978 + -2 x2 = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 x2 = -4.236067978 Simplifying x2 = -4.236067978 Reorder the terms: 4.236067978 + x2 = -4.236067978 + 4.236067978 Combine like terms: -4.236067978 + 4.236067978 = 0.000000000 4.236067978 + 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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