x^4-16x^2-255=0

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Solution for x^4-16x^2-255=0 equation: 


Simplifying
x4 + -16x2 + -255 = 0

Reorder the terms:
-255 + -16x2 + x4 = 0

Solving
-255 + -16x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '255' to each side of the equation.
-255 + -16x2 + 255 + x4 = 0 + 255

Reorder the terms:
-255 + 255 + -16x2 + x4 = 0 + 255

Combine like terms: -255 + 255 = 0
0 + -16x2 + x4 = 0 + 255
-16x2 + x4 = 0 + 255

Combine like terms: 0 + 255 = 255
-16x2 + x4 = 255

The x term is -16x2.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x2 + 64 + x4 = 255 + 64

Reorder the terms:
64 + -16x2 + x4 = 255 + 64

Combine like terms: 255 + 64 = 319
64 + -16x2 + x4 = 319

Factor a perfect square on the left side:
(x2 + -8)(x2 + -8) = 319

Calculate the square root of the right side: 17.860571099

Break this problem into two subproblems by setting 
(x2 + -8) equal to 17.860571099 and -17.860571099.


Subproblem 1
x2 + -8 = 17.860571099

Simplifying
x2 + -8 = 17.860571099

Reorder the terms:
-8 + x2 = 17.860571099

Solving
-8 + x2 = 17.860571099

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x2 = 17.860571099 + 8

Combine like terms: -8 + 8 = 0
0 + x2 = 17.860571099 + 8
x2 = 17.860571099 + 8

Combine like terms: 17.860571099 + 8 = 25.860571099
x2 = 25.860571099

Simplifying
x2 = 25.860571099

Take the square root of each side:
x = {-5.085329006, 5.085329006}


Subproblem 2
x2 + -8 = -17.860571099

Simplifying
x2 + -8 = -17.860571099

Reorder the terms:
-8 + x2 = -17.860571099

Solving
-8 + x2 = -17.860571099

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x2 = -17.860571099 + 8

Combine like terms: -8 + 8 = 0
0 + x2 = -17.860571099 + 8
x2 = -17.860571099 + 8

Combine like terms: -17.860571099 + 8 = -9.860571099
x2 = -9.860571099

Simplifying
x2 = -9.860571099

Reorder the terms:
9.860571099 + x2 = -9.860571099 + 9.860571099

Combine like terms: -9.860571099 + 9.860571099 = 0.000000000
9.860571099 + 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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