2x^4-x^2-28=0

Solution for 2x^4-x^2-28=0 equation:

Simplifying
2x4 + -1x2 + -28 = 0

Reorder the terms:
-28 + -1x2 + 2x4 = 0

Solving
-28 + -1x2 + 2x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -2x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-7 + -2x2)((2 + x)(2 + -1x)) = 0

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

Simplifying
-7 + -2x2 = 0

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

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

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

Divide each side by '-2'.
x2 = -3.5

Simplifying
x2 = -3.5

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}