4x^8-61x^4+225=

Solution for 4x^8-61x^4+225= equation:

Simplifying
4x8 + -61x4 + 225 = 0

Reorder the terms:
225 + -61x4 + 4x8 = 0

Solving
225 + -61x4 + 4x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(25 + -4x4)(9 + -1x4) = 0

Factor a difference between two squares.
((5 + 2x2)(5 + -2x2))(9 + -1x4) = 0

Factor a difference between two squares.
((3 + x2)(3 + -1x2))(5 + 2x2)(5 + -2x2) = 0

Subproblem 1
Set the factor '(5 + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + 2x2 = 0

Solving
5 + 2x2 = 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 + 2x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x2 = 0 + -5
2x2 = 0 + -5

Combine like terms: 0 + -5 = -5
2x2 = -5

Divide each side by '2'.
x2 = -2.5

Simplifying
x2 = -2.5

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 + -2x2)' equal to zero and attempt to solve:

Simplifying
5 + -2x2 = 0

Solving
5 + -2x2 = 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 + -2x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x2 = 0 + -5
-2x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2x2 = -5

Divide each side by '-2'.
x2 = 2.5

Simplifying
x2 = 2.5

Take the square root of each side:
x = {-1.58113883, 1.58113883}
Subproblem 3
Set the factor '(3 + x2)' equal to zero and attempt to solve:

Simplifying
3 + x2 = 0

Solving
3 + x2 = 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 + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x2 = 0 + -3
x2 = 0 + -3

Combine like terms: 0 + -3 = -3
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 4
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

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.58113883, 1.58113883, -1.732050808, 1.732050808}