15x^4-30x^2+7=0

Solution for 15x^4-30x^2+7=0 equation:

Simplifying
15x4 + -30x2 + 7 = 0

Reorder the terms:
7 + -30x2 + 15x4 = 0

Solving
7 + -30x2 + 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'.
0.4666666667 + -2x2 + x4 = 0

Move the constant term to the right:

Add '-0.4666666667' to each side of the equation.
0.4666666667 + -2x2 + -0.4666666667 + x4 = 0 + -0.4666666667

Reorder the terms:
0.4666666667 + -0.4666666667 + -2x2 + x4 = 0 + -0.4666666667

Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000
0.0000000000 + -2x2 + x4 = 0 + -0.4666666667
-2x2 + x4 = 0 + -0.4666666667

Combine like terms: 0 + -0.4666666667 = -0.4666666667
-2x2 + x4 = -0.4666666667

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 = -0.4666666667 + 1

Reorder the terms:
1 + -2x2 + x4 = -0.4666666667 + 1

Combine like terms: -0.4666666667 + 1 = 0.5333333333
1 + -2x2 + x4 = 0.5333333333

Factor a perfect square on the left side:
(x2 + -1)(x2 + -1) = 0.5333333333

Calculate the square root of the right side: 0.730296743

Break this problem into two subproblems by setting 
(x2 + -1) equal to 0.730296743 and -0.730296743.

Subproblem 1
x2 + -1 = 0.730296743

Simplifying
x2 + -1 = 0.730296743

Reorder the terms:
-1 + x2 = 0.730296743

Solving
-1 + x2 = 0.730296743

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 = 0.730296743 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = 0.730296743 + 1
x2 = 0.730296743 + 1

Combine like terms: 0.730296743 + 1 = 1.730296743
x2 = 1.730296743

Simplifying
x2 = 1.730296743

Take the square root of each side:
x = {-1.315407444, 1.315407444}

Subproblem 2
x2 + -1 = -0.730296743

Simplifying
x2 + -1 = -0.730296743

Reorder the terms:
-1 + x2 = -0.730296743

Solving
-1 + x2 = -0.730296743

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 = -0.730296743 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = -0.730296743 + 1
x2 = -0.730296743 + 1

Combine like terms: -0.730296743 + 1 = 0.269703257
x2 = 0.269703257

Simplifying
x2 = 0.269703257

Take the square root of each side:
x = {-0.519329623, 0.519329623}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.315407444, 1.315407444, -0.519329623, 0.519329623}