x^4+36x^2-1944=0

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Solution for x^4+36x^2-1944=0 equation:


Simplifying
x4 + 36x2 + -1944 = 0

Reorder the terms:
-1944 + 36x2 + x4 = 0

Solving
-1944 + 36x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1944' to each side of the equation.
-1944 + 36x2 + 1944 + x4 = 0 + 1944

Reorder the terms:
-1944 + 1944 + 36x2 + x4 = 0 + 1944

Combine like terms: -1944 + 1944 = 0
0 + 36x2 + x4 = 0 + 1944
36x2 + x4 = 0 + 1944

Combine like terms: 0 + 1944 = 1944
36x2 + x4 = 1944

The x term is 36x2.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x2 + 324 + x4 = 1944 + 324

Reorder the terms:
324 + 36x2 + x4 = 1944 + 324

Combine like terms: 1944 + 324 = 2268
324 + 36x2 + x4 = 2268

Factor a perfect square on the left side:
(x2 + 18)(x2 + 18) = 2268

Calculate the square root of the right side: 47.623523599

Break this problem into two subproblems by setting 
(x2 + 18) equal to 47.623523599 and -47.623523599.

Subproblem 1

x2 + 18 = 47.623523599 Simplifying x2 + 18 = 47.623523599 Reorder the terms: 18 + x2 = 47.623523599 Solving 18 + x2 = 47.623523599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x2 = 47.623523599 + -18 Combine like terms: 18 + -18 = 0 0 + x2 = 47.623523599 + -18 x2 = 47.623523599 + -18 Combine like terms: 47.623523599 + -18 = 29.623523599 x2 = 29.623523599 Simplifying x2 = 29.623523599 Take the square root of each side: x = {-5.442749636, 5.442749636}

Subproblem 2

x2 + 18 = -47.623523599 Simplifying x2 + 18 = -47.623523599 Reorder the terms: 18 + x2 = -47.623523599 Solving 18 + x2 = -47.623523599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x2 = -47.623523599 + -18 Combine like terms: 18 + -18 = 0 0 + x2 = -47.623523599 + -18 x2 = -47.623523599 + -18 Combine like terms: -47.623523599 + -18 = -65.623523599 x2 = -65.623523599 Simplifying x2 = -65.623523599 Reorder the terms: 65.623523599 + x2 = -65.623523599 + 65.623523599 Combine like terms: -65.623523599 + 65.623523599 = 0.000000000 65.623523599 + 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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