0=2x^4+15x^2-8

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Solution for 0=2x^4+15x^2-8 equation: 


Simplifying
0 = 2x4 + 15x2 + -8

Reorder the terms:
0 = -8 + 15x2 + 2x4

Solving
0 = -8 + 15x2 + 2x4

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + -15x2 + -2x4 = -8 + 15x2 + 2x4 + 8 + -15x2 + -2x4

Reorder the terms:
8 + -15x2 + -2x4 = -8 + 8 + 15x2 + -15x2 + 2x4 + -2x4

Combine like terms: -8 + 8 = 0
8 + -15x2 + -2x4 = 0 + 15x2 + -15x2 + 2x4 + -2x4
8 + -15x2 + -2x4 = 15x2 + -15x2 + 2x4 + -2x4

Combine like terms: 15x2 + -15x2 = 0
8 + -15x2 + -2x4 = 0 + 2x4 + -2x4
8 + -15x2 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
8 + -15x2 + -2x4 = 0

Factor a trinomial.
(1 + -2x2)(8 + x2) = 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 '(8 + x2)' equal to zero and attempt to solve:

Simplifying
8 + x2 = 0

Solving
8 + x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x2 = 0 + -8
x2 = 0 + -8

Combine like terms: 0 + -8 = -8
x2 = -8

Simplifying
x2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-0.707106781, 0.707106781}

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