x^4-x^2-8=0

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


Simplifying
x4 + -1x2 + -8 = 0

Reorder the terms:
-8 + -1x2 + x4 = 0

Solving
-8 + -1x2 + 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 + -1x2 + 8 + x4 = 0 + 8

Reorder the terms:
-8 + 8 + -1x2 + x4 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x2 + x4 = 0 + 8
-1x2 + x4 = 0 + 8

Combine like terms: 0 + 8 = 8
-1x2 + x4 = 8

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 = 8 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + -1x2 + x4 = 8.25

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
x2 + -0.5 = 2.872281323

Simplifying
x2 + -0.5 = 2.872281323

Reorder the terms:
-0.5 + x2 = 2.872281323

Solving
-0.5 + x2 = 2.872281323

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 = 2.872281323 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 2.872281323 + 0.5
x2 = 2.872281323 + 0.5

Combine like terms: 2.872281323 + 0.5 = 3.372281323
x2 = 3.372281323

Simplifying
x2 = 3.372281323

Take the square root of each side:
x = {-1.836377228, 1.836377228}


Subproblem 2
x2 + -0.5 = -2.872281323

Simplifying
x2 + -0.5 = -2.872281323

Reorder the terms:
-0.5 + x2 = -2.872281323

Solving
-0.5 + x2 = -2.872281323

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 = -2.872281323 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -2.872281323 + 0.5
x2 = -2.872281323 + 0.5

Combine like terms: -2.872281323 + 0.5 = -2.372281323
x2 = -2.372281323

Simplifying
x2 = -2.372281323

Reorder the terms:
2.372281323 + x2 = -2.372281323 + 2.372281323

Combine like terms: -2.372281323 + 2.372281323 = 0.000000000
2.372281323 + 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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