x^4-8x^2=16

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Solution for x^4-8x^2=16 equation: 


Simplifying
x4 + -8x2 = 16

Reorder the terms:
-8x2 + x4 = 16

Solving
-8x2 + x4 = 16

Solving for variable 'x'.

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

Combine like terms: 16 + -16 = 0
-16 + -8x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -8x2 + 16 + x4 = 0 + 16

Reorder the terms:
-16 + 16 + -8x2 + x4 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -8x2 + x4 = 0 + 16
-8x2 + x4 = 0 + 16

Combine like terms: 0 + 16 = 16
-8x2 + x4 = 16

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 = 16 + 16

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

Combine like terms: 16 + 16 = 32
16 + -8x2 + x4 = 32

Factor a perfect square on the left side:
(x2 + -4)(x2 + -4) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x2 + -4) equal to 5.656854249 and -5.656854249.


Subproblem 1
x2 + -4 = 5.656854249

Simplifying
x2 + -4 = 5.656854249

Reorder the terms:
-4 + x2 = 5.656854249

Solving
-4 + x2 = 5.656854249

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 = 5.656854249 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = 5.656854249 + 4
x2 = 5.656854249 + 4

Combine like terms: 5.656854249 + 4 = 9.656854249
x2 = 9.656854249

Simplifying
x2 = 9.656854249

Take the square root of each side:
x = {-3.107547948, 3.107547948}


Subproblem 2
x2 + -4 = -5.656854249

Simplifying
x2 + -4 = -5.656854249

Reorder the terms:
-4 + x2 = -5.656854249

Solving
-4 + x2 = -5.656854249

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 = -5.656854249 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = -5.656854249 + 4
x2 = -5.656854249 + 4

Combine like terms: -5.656854249 + 4 = -1.656854249
x2 = -1.656854249

Simplifying
x2 = -1.656854249

Reorder the terms:
1.656854249 + x2 = -1.656854249 + 1.656854249

Combine like terms: -1.656854249 + 1.656854249 = 0.000000000
1.656854249 + 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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