2x^4+16x^2=40

Solution for 2x^4+16x^2=40 equation:

Simplifying
2x4 + 16x2 = 40

Reorder the terms:
16x2 + 2x4 = 40

Solving
16x2 + 2x4 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 16x2 + 2x4 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 16x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 8x2 + x4) = 0

Factor a trinomial.
2((-10 + -1x2)(2 + -1x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -1x2)' equal to zero and attempt to solve:

Simplifying
-10 + -1x2 = 0

Solving
-10 + -1x2 = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x2 = 0 + 10
-1x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1x2 = 10

Divide each side by '-1'.
x2 = -10

Simplifying
x2 = -10

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 '(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}
Solution
x = {-1.414213562, 1.414213562}