0=x^4+6x^2-16

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Solution for 0=x^4+6x^2-16 equation: 


Simplifying
0 = x4 + 6x2 + -16

Reorder the terms:
0 = -16 + 6x2 + x4

Solving
0 = -16 + 6x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 16 = 16
16 + -6x2 + -1x4 = -16 + 6x2 + x4 + 16 + -6x2 + -1x4

Reorder the terms:
16 + -6x2 + -1x4 = -16 + 16 + 6x2 + -6x2 + x4 + -1x4

Combine like terms: -16 + 16 = 0
16 + -6x2 + -1x4 = 0 + 6x2 + -6x2 + x4 + -1x4
16 + -6x2 + -1x4 = 6x2 + -6x2 + x4 + -1x4

Combine like terms: 6x2 + -6x2 = 0
16 + -6x2 + -1x4 = 0 + x4 + -1x4
16 + -6x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
16 + -6x2 + -1x4 = 0

Factor a trinomial.
(2 + -1x2)(8 + x2) = 0


Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}

Subproblem 2
Set the factor '(8 + x2)' equal to zero and attempt to solve:

Simplifying
8 + x2 = 0

Solving
8 + x2 = 0

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 = 0 + -8

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

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

Simplifying
x2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-1.414213562, 1.414213562}

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