x^4-12x^2-324=0

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Solution for x^4-12x^2-324=0 equation:


Simplifying
x4 + -12x2 + -324 = 0

Reorder the terms:
-324 + -12x2 + x4 = 0

Solving
-324 + -12x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '324' to each side of the equation.
-324 + -12x2 + 324 + x4 = 0 + 324

Reorder the terms:
-324 + 324 + -12x2 + x4 = 0 + 324

Combine like terms: -324 + 324 = 0
0 + -12x2 + x4 = 0 + 324
-12x2 + x4 = 0 + 324

Combine like terms: 0 + 324 = 324
-12x2 + x4 = 324

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 = 324 + 36

Reorder the terms:
36 + -12x2 + x4 = 324 + 36

Combine like terms: 324 + 36 = 360
36 + -12x2 + x4 = 360

Factor a perfect square on the left side:
(x2 + -6)(x2 + -6) = 360

Calculate the square root of the right side: 18.973665961

Break this problem into two subproblems by setting 
(x2 + -6) equal to 18.973665961 and -18.973665961.

Subproblem 1

x2 + -6 = 18.973665961 Simplifying x2 + -6 = 18.973665961 Reorder the terms: -6 + x2 = 18.973665961 Solving -6 + x2 = 18.973665961 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 = 18.973665961 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 18.973665961 + 6 x2 = 18.973665961 + 6 Combine like terms: 18.973665961 + 6 = 24.973665961 x2 = 24.973665961 Simplifying x2 = 24.973665961 Take the square root of each side: x = {-4.997365902, 4.997365902}

Subproblem 2

x2 + -6 = -18.973665961 Simplifying x2 + -6 = -18.973665961 Reorder the terms: -6 + x2 = -18.973665961 Solving -6 + x2 = -18.973665961 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 = -18.973665961 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -18.973665961 + 6 x2 = -18.973665961 + 6 Combine like terms: -18.973665961 + 6 = -12.973665961 x2 = -12.973665961 Simplifying x2 = -12.973665961 Reorder the terms: 12.973665961 + x2 = -12.973665961 + 12.973665961 Combine like terms: -12.973665961 + 12.973665961 = 0.000000000 12.973665961 + 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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