0=15x^4-30x^2+1

Solution for 0=15x^4-30x^2+1 equation:

Simplifying
0 = 15x4 + -30x2 + 1

Reorder the terms:
0 = 1 + -30x2 + 15x4

Solving
0 = 1 + -30x2 + 15x4

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 30x2 + -15x4 = 1 + -30x2 + 15x4 + -1 + 30x2 + -15x4

Reorder the terms:
-1 + 30x2 + -15x4 = 1 + -1 + -30x2 + 30x2 + 15x4 + -15x4

Combine like terms: 1 + -1 = 0
-1 + 30x2 + -15x4 = 0 + -30x2 + 30x2 + 15x4 + -15x4
-1 + 30x2 + -15x4 = -30x2 + 30x2 + 15x4 + -15x4

Combine like terms: -30x2 + 30x2 = 0
-1 + 30x2 + -15x4 = 0 + 15x4 + -15x4
-1 + 30x2 + -15x4 = 15x4 + -15x4

Combine like terms: 15x4 + -15x4 = 0
-1 + 30x2 + -15x4 = 0

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

Divide each side by '-15'.
0.06666666667 + -2x2 + x4 = 0

Move the constant term to the right:

Add '-0.06666666667' to each side of the equation.
0.06666666667 + -2x2 + -0.06666666667 + x4 = 0 + -0.06666666667

Reorder the terms:
0.06666666667 + -0.06666666667 + -2x2 + x4 = 0 + -0.06666666667

Combine like terms: 0.06666666667 + -0.06666666667 = 0.00000000000
0.00000000000 + -2x2 + x4 = 0 + -0.06666666667
-2x2 + x4 = 0 + -0.06666666667

Combine like terms: 0 + -0.06666666667 = -0.06666666667
-2x2 + x4 = -0.06666666667

The x term is -2x2.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x2 + 1 + x4 = -0.06666666667 + 1

Reorder the terms:
1 + -2x2 + x4 = -0.06666666667 + 1

Combine like terms: -0.06666666667 + 1 = 0.93333333333
1 + -2x2 + x4 = 0.93333333333

Factor a perfect square on the left side:
(x2 + -1)(x2 + -1) = 0.93333333333

Calculate the square root of the right side: 0.966091783

Break this problem into two subproblems by setting 
(x2 + -1) equal to 0.966091783 and -0.966091783.

Subproblem 1
x2 + -1 = 0.966091783

Simplifying
x2 + -1 = 0.966091783

Reorder the terms:
-1 + x2 = 0.966091783

Solving
-1 + x2 = 0.966091783

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x2 = 0.966091783 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = 0.966091783 + 1
x2 = 0.966091783 + 1

Combine like terms: 0.966091783 + 1 = 1.966091783
x2 = 1.966091783

Simplifying
x2 = 1.966091783

Take the square root of each side:
x = {-1.402173949, 1.402173949}

Subproblem 2
x2 + -1 = -0.966091783

Simplifying
x2 + -1 = -0.966091783

Reorder the terms:
-1 + x2 = -0.966091783

Solving
-1 + x2 = -0.966091783

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x2 = -0.966091783 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = -0.966091783 + 1
x2 = -0.966091783 + 1

Combine like terms: -0.966091783 + 1 = 0.033908217
x2 = 0.033908217

Simplifying
x2 = 0.033908217

Take the square root of each side:
x = {-0.184141839, 0.184141839}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.402173949, 1.402173949, -0.184141839, 0.184141839}