20x^4-21x^2+1=0

Solution for 20x^4-21x^2+1=0 equation:

Simplifying
20x4 + -21x2 + 1 = 0

Reorder the terms:
1 + -21x2 + 20x4 = 0

Solving
1 + -21x2 + 20x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -20x2)(1 + -1x2) = 0

Factor a difference between two squares.
(1 + -20x2)((1 + x)(1 + -1x)) = 0

Subproblem 1
Set the factor '(1 + -20x2)' equal to zero and attempt to solve:

Simplifying
1 + -20x2 = 0

Solving
1 + -20x2 = 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 + -20x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -20x2 = 0 + -1
-20x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-20x2 = -1

Divide each side by '-20'.
x2 = 0.05

Simplifying
x2 = 0.05

Take the square root of each side:
x = {-0.223606798, 0.223606798}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.223606798, 0.223606798, -1, 1}