5x^4-22x^2+21=0

Solution for 5x^4-22x^2+21=0 equation:

Simplifying
5x4 + -22x2 + 21 = 0

Reorder the terms:
21 + -22x2 + 5x4 = 0

Solving
21 + -22x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -5x2)(3 + -1x2) = 0

Subproblem 1
Set the factor '(7 + -5x2)' equal to zero and attempt to solve:

Simplifying
7 + -5x2 = 0

Solving
7 + -5x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x2 = 0 + -7
-5x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-5x2 = -7

Divide each side by '-5'.
x2 = 1.4

Simplifying
x2 = 1.4

Take the square root of each side:
x = {-1.183215957, 1.183215957}
Subproblem 2
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 = {-1.183215957, 1.183215957, -1.732050808, 1.732050808}