x^4-181*x^2-8280=0

Solution for x^4-181*x^2-8280=0 equation:

Simplifying
x4 + -181x2 + -8280 = 0

Reorder the terms:
-8280 + -181x2 + x4 = 0

Solving
-8280 + -181x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8280' to each side of the equation.
-8280 + -181x2 + 8280 + x4 = 0 + 8280

Reorder the terms:
-8280 + 8280 + -181x2 + x4 = 0 + 8280

Combine like terms: -8280 + 8280 = 0
0 + -181x2 + x4 = 0 + 8280
-181x2 + x4 = 0 + 8280

Combine like terms: 0 + 8280 = 8280
-181x2 + x4 = 8280

The x term is -181x2.  Take half its coefficient (-90.5).
Square it (8190.25) and add it to both sides.

Add '8190.25' to each side of the equation.
-181x2 + 8190.25 + x4 = 8280 + 8190.25

Reorder the terms:
8190.25 + -181x2 + x4 = 8280 + 8190.25

Combine like terms: 8280 + 8190.25 = 16470.25
8190.25 + -181x2 + x4 = 16470.25

Factor a perfect square on the left side:
(x2 + -90.5)(x2 + -90.5) = 16470.25

Calculate the square root of the right side: 128.336471823

Break this problem into two subproblems by setting 
(x2 + -90.5) equal to 128.336471823 and -128.336471823.

Subproblem 1
x2 + -90.5 = 128.336471823

Simplifying
x2 + -90.5 = 128.336471823

Reorder the terms:
-90.5 + x2 = 128.336471823

Solving
-90.5 + x2 = 128.336471823

Solving for variable 'x'.

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

Add '90.5' to each side of the equation.
-90.5 + 90.5 + x2 = 128.336471823 + 90.5

Combine like terms: -90.5 + 90.5 = 0.0
0.0 + x2 = 128.336471823 + 90.5
x2 = 128.336471823 + 90.5

Combine like terms: 128.336471823 + 90.5 = 218.836471823
x2 = 218.836471823

Simplifying
x2 = 218.836471823

Take the square root of each side:
x = {-14.79312245, 14.79312245}

Subproblem 2
x2 + -90.5 = -128.336471823

Simplifying
x2 + -90.5 = -128.336471823

Reorder the terms:
-90.5 + x2 = -128.336471823

Solving
-90.5 + x2 = -128.336471823

Solving for variable 'x'.

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

Add '90.5' to each side of the equation.
-90.5 + 90.5 + x2 = -128.336471823 + 90.5

Combine like terms: -90.5 + 90.5 = 0.0
0.0 + x2 = -128.336471823 + 90.5
x2 = -128.336471823 + 90.5

Combine like terms: -128.336471823 + 90.5 = -37.836471823
x2 = -37.836471823

Simplifying
x2 = -37.836471823

Reorder the terms:
37.836471823 + x2 = -37.836471823 + 37.836471823

Combine like terms: -37.836471823 + 37.836471823 = 0.000000000
37.836471823 + 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.