2x^4-102x^2=-196

Solution for 2x^4-102x^2=-196 equation:

Simplifying
2x4 + -102x2 = -196

Reorder the terms:
-102x2 + 2x4 = -196

Solving
-102x2 + 2x4 = -196

Solving for variable 'x'.

Reorder the terms:
196 + -102x2 + 2x4 = -196 + 196

Combine like terms: -196 + 196 = 0
196 + -102x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(98 + -51x2 + x4) = 0

Factor a trinomial.
2((2 + -1x2)(49 + -1x2)) = 0

Factor a difference between two squares.
2((2 + -1x2)((7 + x)(7 + -1x))) = 0

Ignore the factor 2.
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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.414213562, 1.414213562, -7, 7}