-2x^4+46x^2=-100

Solution for -2x^4+46x^2=-100 equation:

Simplifying
-2x4 + 46x2 = -100

Reorder the terms:
46x2 + -2x4 = -100

Solving
46x2 + -2x4 = -100

Solving for variable 'x'.

Reorder the terms:
100 + 46x2 + -2x4 = -100 + 100

Combine like terms: -100 + 100 = 0
100 + 46x2 + -2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(50 + 23x2 + -1x4) = 0

Factor a trinomial.
2((25 + -1x2)(2 + x2)) = 0

Factor a difference between two squares.
2(((5 + x)(5 + -1x))(2 + x2)) = 0

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

Simplifying
2 + x2 = 0

Solving
2 + x2 = 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 + x2 = 0 + -2

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

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

Simplifying
x2 = -2

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-5, 5}