a^4-6a^2+4=0

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Solution for a^4-6a^2+4=0 equation:


Simplifying
a4 + -6a2 + 4 = 0

Reorder the terms:
4 + -6a2 + a4 = 0

Solving
4 + -6a2 + a4 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6a2 + -4 + a4 = 0 + -4

Reorder the terms:
4 + -4 + -6a2 + a4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6a2 + a4 = 0 + -4
-6a2 + a4 = 0 + -4

Combine like terms: 0 + -4 = -4
-6a2 + a4 = -4

The a term is -6a2.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a2 + 9 + a4 = -4 + 9

Reorder the terms:
9 + -6a2 + a4 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6a2 + a4 = 5

Factor a perfect square on the left side:
(a2 + -3)(a2 + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(a2 + -3) equal to 2.236067978 and -2.236067978.

Subproblem 1

a2 + -3 = 2.236067978 Simplifying a2 + -3 = 2.236067978 Reorder the terms: -3 + a2 = 2.236067978 Solving -3 + a2 = 2.236067978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a2 = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + a2 = 2.236067978 + 3 a2 = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 a2 = 5.236067978 Simplifying a2 = 5.236067978 Take the square root of each side: a = {-2.288245611, 2.288245611}

Subproblem 2

a2 + -3 = -2.236067978 Simplifying a2 + -3 = -2.236067978 Reorder the terms: -3 + a2 = -2.236067978 Solving -3 + a2 = -2.236067978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a2 = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + a2 = -2.236067978 + 3 a2 = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 a2 = 0.763932022 Simplifying a2 = 0.763932022 Take the square root of each side: a = {-0.874032049, 0.874032049}

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-2.288245611, 2.288245611, -0.874032049, 0.874032049}

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