21x^4=2+x^2

Solution for 21x^4=2+x^2 equation:

Simplifying
21x4 = 2 + x2

Solving
21x4 = 2 + x2

Solving for variable 'x'.

Reorder the terms:
-2 + -1x2 + 21x4 = 2 + x2 + -2 + -1x2

Reorder the terms:
-2 + -1x2 + 21x4 = 2 + -2 + x2 + -1x2

Combine like terms: 2 + -2 = 0
-2 + -1x2 + 21x4 = 0 + x2 + -1x2
-2 + -1x2 + 21x4 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + -1x2 + 21x4 = 0

Factor a trinomial.
(-2 + -7x2)(1 + -3x2) = 0

Subproblem 1
Set the factor '(-2 + -7x2)' equal to zero and attempt to solve:

Simplifying
-2 + -7x2 = 0

Solving
-2 + -7x2 = 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 + -7x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7x2 = 0 + 2
-7x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-7x2 = 2

Divide each side by '-7'.
x2 = -0.2857142857

Simplifying
x2 = -0.2857142857

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 + -3x2)' equal to zero and attempt to solve:

Simplifying
1 + -3x2 = 0

Solving
1 + -3x2 = 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 + -3x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x2 = 0 + -1
-3x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3x2 = -1

Divide each side by '-3'.
x2 = 0.3333333333

Simplifying
x2 = 0.3333333333

Take the square root of each side:
x = {-0.577350269, 0.577350269}
Solution
x = {-0.577350269, 0.577350269}