x^4+9x^2=52

Solution for x^4+9x^2=52 equation:

Simplifying
x4 + 9x2 = 52

Reorder the terms:
9x2 + x4 = 52

Solving
9x2 + x4 = 52

Solving for variable 'x'.

Reorder the terms:
-52 + 9x2 + x4 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + 9x2 + x4 = 0

Factor a trinomial.
(-13 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-13 + -1x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(-13 + -1x2)' equal to zero and attempt to solve:

Simplifying
-13 + -1x2 = 0

Solving
-13 + -1x2 = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x2 = 0 + 13
-1x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-1x2 = 13

Divide each side by '-1'.
x2 = -13

Simplifying
x2 = -13

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

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

Simplifying
x = 2
Solution
x = {-2, 2}