2x^4-14x^2=16

Solution for 2x^4-14x^2=16 equation:

Simplifying
2x4 + -14x2 = 16

Reorder the terms:
-14x2 + 2x4 = 16

Solving
-14x2 + 2x4 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + -14x2 + 2x4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -14x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -7x2 + x4) = 0

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

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

Simplifying
-1 + -1x2 = 0

Solving
-1 + -1x2 = 0

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

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

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

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

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

Simplifying
x2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(8 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

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

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

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

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}
Solution
x = {-2.828427125, 2.828427125}