5x^4-89x^2-900=0

Solution for 5x^4-89x^2-900=0 equation:

Simplifying
5x4 + -89x2 + -900 = 0

Reorder the terms:
-900 + -89x2 + 5x4 = 0

Solving
-900 + -89x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-36 + -5x2)(25 + -1x2) = 0

Factor a difference between two squares.
(-36 + -5x2)((5 + x)(5 + -1x)) = 0

Subproblem 1
Set the factor '(-36 + -5x2)' equal to zero and attempt to solve:

Simplifying
-36 + -5x2 = 0

Solving
-36 + -5x2 = 0

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

Add '36' to each side of the equation.
-36 + 36 + -5x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -5x2 = 0 + 36
-5x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-5x2 = 36

Divide each side by '-5'.
x2 = -7.2

Simplifying
x2 = -7.2

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}