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

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


Simplifying
x4 + -12x2 + -2 = 0

Reorder the terms:
-2 + -12x2 + x4 = 0

Solving
-2 + -12x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -12x2 + 2 + x4 = 0 + 2

Reorder the terms:
-2 + 2 + -12x2 + x4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -12x2 + x4 = 0 + 2
-12x2 + x4 = 0 + 2

Combine like terms: 0 + 2 = 2
-12x2 + x4 = 2

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 = 2 + 36

Reorder the terms:
36 + -12x2 + x4 = 2 + 36

Combine like terms: 2 + 36 = 38
36 + -12x2 + x4 = 38

Factor a perfect square on the left side:
(x2 + -6)(x2 + -6) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x2 + -6) equal to 6.164414003 and -6.164414003.

Subproblem 1

x2 + -6 = 6.164414003 Simplifying x2 + -6 = 6.164414003 Reorder the terms: -6 + x2 = 6.164414003 Solving -6 + x2 = 6.164414003 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 = 6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 6.164414003 + 6 x2 = 6.164414003 + 6 Combine like terms: 6.164414003 + 6 = 12.164414003 x2 = 12.164414003 Simplifying x2 = 12.164414003 Take the square root of each side: x = {-3.487751998, 3.487751998}

Subproblem 2

x2 + -6 = -6.164414003 Simplifying x2 + -6 = -6.164414003 Reorder the terms: -6 + x2 = -6.164414003 Solving -6 + x2 = -6.164414003 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 = -6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -6.164414003 + 6 x2 = -6.164414003 + 6 Combine like terms: -6.164414003 + 6 = -0.164414003 x2 = -0.164414003 Simplifying x2 = -0.164414003 Reorder the terms: 0.164414003 + x2 = -0.164414003 + 0.164414003 Combine like terms: -0.164414003 + 0.164414003 = 0.000000000 0.164414003 + 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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