5x^4=2-9x^2

Solution for 5x^4=2-9x^2 equation:

Simplifying
5x4 = 2 + -9x2

Solving
5x4 = 2 + -9x2

Solving for variable 'x'.

Reorder the terms:
-2 + 9x2 + 5x4 = 2 + -9x2 + -2 + 9x2

Reorder the terms:
-2 + 9x2 + 5x4 = 2 + -2 + -9x2 + 9x2

Combine like terms: 2 + -2 = 0
-2 + 9x2 + 5x4 = 0 + -9x2 + 9x2
-2 + 9x2 + 5x4 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-2 + 9x2 + 5x4 = 0

Factor a trinomial.
(-2 + -1x2)(1 + -5x2) = 0

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

Simplifying
-2 + -1x2 = 0

Solving
-2 + -1x2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x2 = 0 + 2
-1x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1x2 = 2

Divide each side by '-1'.
x2 = -2

Simplifying
x2 = -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 '(1 + -5x2)' equal to zero and attempt to solve:

Simplifying
1 + -5x2 = 0

Solving
1 + -5x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x2 = 0 + -1
-5x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5x2 = -1

Divide each side by '-5'.
x2 = 0.2

Simplifying
x2 = 0.2

Take the square root of each side:
x = {-0.447213596, 0.447213596}
Solution
x = {-0.447213596, 0.447213596}