x^4-33x^2-200=0

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Solution for x^4-33x^2-200=0 equation: 


Simplifying
x4 + -33x2 + -200 = 0

Reorder the terms:
-200 + -33x2 + x4 = 0

Solving
-200 + -33x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + -33x2 + 200 + x4 = 0 + 200

Reorder the terms:
-200 + 200 + -33x2 + x4 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -33x2 + x4 = 0 + 200
-33x2 + x4 = 0 + 200

Combine like terms: 0 + 200 = 200
-33x2 + x4 = 200

The x term is -33x2.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33x2 + 272.25 + x4 = 200 + 272.25

Reorder the terms:
272.25 + -33x2 + x4 = 200 + 272.25

Combine like terms: 200 + 272.25 = 472.25
272.25 + -33x2 + x4 = 472.25

Factor a perfect square on the left side:
(x2 + -16.5)(x2 + -16.5) = 472.25

Calculate the square root of the right side: 21.731313812

Break this problem into two subproblems by setting 
(x2 + -16.5) equal to 21.731313812 and -21.731313812.


Subproblem 1
x2 + -16.5 = 21.731313812

Simplifying
x2 + -16.5 = 21.731313812

Reorder the terms:
-16.5 + x2 = 21.731313812

Solving
-16.5 + x2 = 21.731313812

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '16.5' to each side of the equation.
-16.5 + 16.5 + x2 = 21.731313812 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x2 = 21.731313812 + 16.5
x2 = 21.731313812 + 16.5

Combine like terms: 21.731313812 + 16.5 = 38.231313812
x2 = 38.231313812

Simplifying
x2 = 38.231313812

Take the square root of each side:
x = {-6.183147565, 6.183147565}


Subproblem 2
x2 + -16.5 = -21.731313812

Simplifying
x2 + -16.5 = -21.731313812

Reorder the terms:
-16.5 + x2 = -21.731313812

Solving
-16.5 + x2 = -21.731313812

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '16.5' to each side of the equation.
-16.5 + 16.5 + x2 = -21.731313812 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x2 = -21.731313812 + 16.5
x2 = -21.731313812 + 16.5

Combine like terms: -21.731313812 + 16.5 = -5.231313812
x2 = -5.231313812

Simplifying
x2 = -5.231313812

Reorder the terms:
5.231313812 + x2 = -5.231313812 + 5.231313812

Combine like terms: -5.231313812 + 5.231313812 = 0.000000000
5.231313812 + 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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