8x^4-22x^2+9=0

Solution for 8x^4-22x^2+9=0 equation:

Simplifying
8x4 + -22x2 + 9 = 0

Reorder the terms:
9 + -22x2 + 8x4 = 0

Solving
9 + -22x2 + 8x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x2)(9 + -4x2) = 0

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

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

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 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 + -2x2 = 0 + -1

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

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

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.707106781, 0.707106781, -1.5, 1.5}