X^4-13X^2-48=0

Solution for X^4-13X^2-48=0 equation:

Simplifying
X4 + -13X2 + -48 = 0

Reorder the terms:
-48 + -13X2 + X4 = 0

Solving
-48 + -13X2 + X4 = 0

Solving for variable 'X'.

Factor a trinomial.
(-3 + -1X2)(16 + -1X2) = 0

Factor a difference between two squares.
(-3 + -1X2)((4 + X)(4 + -1X)) = 0

Subproblem 1
Set the factor '(-3 + -1X2)' equal to zero and attempt to solve:

Simplifying
-3 + -1X2 = 0

Solving
-3 + -1X2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1X2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1X2 = 0 + 3
-1X2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1X2 = 3

Divide each side by '-1'.
X2 = -3

Simplifying
X2 = -3

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 '(4 + X)' equal to zero and attempt to solve:

Simplifying
4 + X = 0

Solving
4 + X = 0

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

Add '-4' to each side of the equation.
4 + -4 + X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + X = 0 + -4
X = 0 + -4

Combine like terms: 0 + -4 = -4
X = -4

Simplifying
X = -4
Subproblem 3
Set the factor '(4 + -1X)' equal to zero and attempt to solve:

Simplifying
4 + -1X = 0

Solving
4 + -1X = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1X = 0 + -4
-1X = 0 + -4

Combine like terms: 0 + -4 = -4
-1X = -4

Divide each side by '-1'.
X = 4

Simplifying
X = 4
Solution
X = {-4, 4}