x^4-48x^2-100=0

Solution for x^4-48x^2-100=0 equation:

Simplifying
x4 + -48x2 + -100 = 0

Reorder the terms:
-100 + -48x2 + x4 = 0

Solving
-100 + -48x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x2)(50 + -1x2) = 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

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 '(50 + -1x2)' equal to zero and attempt to solve:

Simplifying
50 + -1x2 = 0

Solving
50 + -1x2 = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x2 = 0 + -50
-1x2 = 0 + -50

Combine like terms: 0 + -50 = -50
-1x2 = -50

Divide each side by '-1'.
x2 = 50

Simplifying
x2 = 50

Take the square root of each side:
x = {-7.071067812, 7.071067812}
Solution
x = {-7.071067812, 7.071067812}