4x^4-31x^2-45=0

Solution for 4x^4-31x^2-45=0 equation:

Simplifying
4x4 + -31x2 + -45 = 0

Reorder the terms:
-45 + -31x2 + 4x4 = 0

Solving
-45 + -31x2 + 4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -4x2)(9 + -1x2) = 0

Factor a difference between two squares.
(-5 + -4x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(-5 + -4x2)' equal to zero and attempt to solve:

Simplifying
-5 + -4x2 = 0

Solving
-5 + -4x2 = 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 + -4x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x2 = 0 + 5
-4x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-4x2 = 5

Divide each side by '-4'.
x2 = -1.25

Simplifying
x2 = -1.25

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

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

Simplifying
x = 3
Solution
x = {-3, 3}