(x^4)-(x^2)-396=0

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Solution for (x^4)-(x^2)-396=0 equation: 


Simplifying
(x4) + -1(x2) + -396 = 0
x4 + -1(x2) + -396 = 0

Reorder the terms:
-396 + -1x2 + x4 = 0

Solving
-396 + -1x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '396' to each side of the equation.
-396 + -1x2 + 396 + x4 = 0 + 396

Reorder the terms:
-396 + 396 + -1x2 + x4 = 0 + 396

Combine like terms: -396 + 396 = 0
0 + -1x2 + x4 = 0 + 396
-1x2 + x4 = 0 + 396

Combine like terms: 0 + 396 = 396
-1x2 + x4 = 396

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = 396 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 396 + 0.25

Combine like terms: 396 + 0.25 = 396.25
0.25 + -1x2 + x4 = 396.25

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 396.25

Calculate the square root of the right side: 19.906029237

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 19.906029237 and -19.906029237.


Subproblem 1
x2 + -0.5 = 19.906029237

Simplifying
x2 + -0.5 = 19.906029237

Reorder the terms:
-0.5 + x2 = 19.906029237

Solving
-0.5 + x2 = 19.906029237

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = 19.906029237 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 19.906029237 + 0.5
x2 = 19.906029237 + 0.5

Combine like terms: 19.906029237 + 0.5 = 20.406029237
x2 = 20.406029237

Simplifying
x2 = 20.406029237

Take the square root of each side:
x = {-4.517303315, 4.517303315}


Subproblem 2
x2 + -0.5 = -19.906029237

Simplifying
x2 + -0.5 = -19.906029237

Reorder the terms:
-0.5 + x2 = -19.906029237

Solving
-0.5 + x2 = -19.906029237

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = -19.906029237 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -19.906029237 + 0.5
x2 = -19.906029237 + 0.5

Combine like terms: -19.906029237 + 0.5 = -19.406029237
x2 = -19.406029237

Simplifying
x2 = -19.406029237

Reorder the terms:
19.406029237 + x2 = -19.406029237 + 19.406029237

Combine like terms: -19.406029237 + 19.406029237 = 0.000000000
19.406029237 + 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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