2X^4-225+7X^2=0

Solution for 2X^4-225+7X^2=0 equation:

Simplifying
2X4 + -225 + 7X2 = 0

Reorder the terms:
-225 + 7X2 + 2X4 = 0

Solving
-225 + 7X2 + 2X4 = 0

Solving for variable 'X'.

Factor a trinomial.
(-25 + -2X2)(9 + -1X2) = 0

Factor a difference between two squares.
(-25 + -2X2)((3 + X)(3 + -1X)) = 0

Subproblem 1
Set the factor '(-25 + -2X2)' equal to zero and attempt to solve:

Simplifying
-25 + -2X2 = 0

Solving
-25 + -2X2 = 0

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

Add '25' to each side of the equation.
-25 + 25 + -2X2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2X2 = 0 + 25
-2X2 = 0 + 25

Combine like terms: 0 + 25 = 25
-2X2 = 25

Divide each side by '-2'.
X2 = -12.5

Simplifying
X2 = -12.5

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 '(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}