x^4-12x^2+16=0

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Solution for x^4-12x^2+16=0 equation:


Simplifying
x4 + -12x2 + 16 = 0

Reorder the terms:
16 + -12x2 + x4 = 0

Solving
16 + -12x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -12x2 + -16 + x4 = 0 + -16

Reorder the terms:
16 + -16 + -12x2 + x4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -12x2 + x4 = 0 + -16
-12x2 + x4 = 0 + -16

Combine like terms: 0 + -16 = -16
-12x2 + x4 = -16

The x term is -12x2.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x2 + 36 + x4 = -16 + 36

Reorder the terms:
36 + -12x2 + x4 = -16 + 36

Combine like terms: -16 + 36 = 20
36 + -12x2 + x4 = 20

Factor a perfect square on the left side:
(x2 + -6)(x2 + -6) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x2 + -6) equal to 4.472135955 and -4.472135955.

Subproblem 1

x2 + -6 = 4.472135955 Simplifying x2 + -6 = 4.472135955 Reorder the terms: -6 + x2 = 4.472135955 Solving -6 + x2 = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = 4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 4.472135955 + 6 x2 = 4.472135955 + 6 Combine like terms: 4.472135955 + 6 = 10.472135955 x2 = 10.472135955 Simplifying x2 = 10.472135955 Take the square root of each side: x = {-3.236067978, 3.236067978}

Subproblem 2

x2 + -6 = -4.472135955 Simplifying x2 + -6 = -4.472135955 Reorder the terms: -6 + x2 = -4.472135955 Solving -6 + x2 = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = -4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -4.472135955 + 6 x2 = -4.472135955 + 6 Combine like terms: -4.472135955 + 6 = 1.527864045 x2 = 1.527864045 Simplifying x2 = 1.527864045 Take the square root of each side: x = {-1.236067978, 1.236067978}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.236067978, 3.236067978, -1.236067978, 1.236067978}

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