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

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

Simplifying
15x4 + -15x2 + 2 = 0

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

Solving
2 + -15x2 + 15x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
0.1333333333 + -1x2 + x4 = 0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + -1x2 + -0.1333333333 + x4 = 0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + -1x2 + x4 = 0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + -1x2 + x4 = 0 + -0.1333333333
-1x2 + x4 = 0 + -0.1333333333

Combine like terms: 0 + -0.1333333333 = -0.1333333333
-1x2 + x4 = -0.1333333333

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = -0.1333333333 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = -0.1333333333 + 0.25

Combine like terms: -0.1333333333 + 0.25 = 0.1166666667
0.25 + -1x2 + x4 = 0.1166666667

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 0.1166666667

Calculate the square root of the right side: 0.341565026

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 0.341565026 and -0.341565026.

Subproblem 1
x2 + -0.5 = 0.341565026

Simplifying
x2 + -0.5 = 0.341565026

Reorder the terms:
-0.5 + x2 = 0.341565026

Solving
-0.5 + x2 = 0.341565026

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = 0.341565026 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 0.341565026 + 0.5
x2 = 0.341565026 + 0.5

Combine like terms: 0.341565026 + 0.5 = 0.841565026
x2 = 0.841565026

Simplifying
x2 = 0.841565026

Take the square root of each side:
x = {-0.917368533, 0.917368533}

Subproblem 2
x2 + -0.5 = -0.341565026

Simplifying
x2 + -0.5 = -0.341565026

Reorder the terms:
-0.5 + x2 = -0.341565026

Solving
-0.5 + x2 = -0.341565026

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = -0.341565026 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -0.341565026 + 0.5
x2 = -0.341565026 + 0.5

Combine like terms: -0.341565026 + 0.5 = 0.158434974
x2 = 0.158434974

Simplifying
x2 = 0.158434974

Take the square root of each side:
x = {-0.39803891, 0.39803891}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.917368533, 0.917368533, -0.39803891, 0.39803891}