x^4-8x^2-8=0

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Solution for x^4-8x^2-8=0 equation: 


Simplifying
x4 + -8x2 + -8 = 0

Reorder the terms:
-8 + -8x2 + x4 = 0

Solving
-8 + -8x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -8x2 + 8 + x4 = 0 + 8

Reorder the terms:
-8 + 8 + -8x2 + x4 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -8x2 + x4 = 0 + 8
-8x2 + x4 = 0 + 8

Combine like terms: 0 + 8 = 8
-8x2 + x4 = 8

The x term is -8x2.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x2 + 16 + x4 = 8 + 16

Reorder the terms:
16 + -8x2 + x4 = 8 + 16

Combine like terms: 8 + 16 = 24
16 + -8x2 + x4 = 24

Factor a perfect square on the left side:
(x2 + -4)(x2 + -4) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x2 + -4) equal to 4.898979486 and -4.898979486.


Subproblem 1
x2 + -4 = 4.898979486

Simplifying
x2 + -4 = 4.898979486

Reorder the terms:
-4 + x2 = 4.898979486

Solving
-4 + x2 = 4.898979486

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = 4.898979486 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = 4.898979486 + 4
x2 = 4.898979486 + 4

Combine like terms: 4.898979486 + 4 = 8.898979486
x2 = 8.898979486

Simplifying
x2 = 8.898979486

Take the square root of each side:
x = {-2.983115735, 2.983115735}


Subproblem 2
x2 + -4 = -4.898979486

Simplifying
x2 + -4 = -4.898979486

Reorder the terms:
-4 + x2 = -4.898979486

Solving
-4 + x2 = -4.898979486

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = -4.898979486 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = -4.898979486 + 4
x2 = -4.898979486 + 4

Combine like terms: -4.898979486 + 4 = -0.898979486
x2 = -0.898979486

Simplifying
x2 = -0.898979486

Reorder the terms:
0.898979486 + x2 = -0.898979486 + 0.898979486

Combine like terms: -0.898979486 + 0.898979486 = 0.000000000
0.898979486 + 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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