25x^4-55x^2+15=0

Solution for 25x^4-55x^2+15=0 equation:

Simplifying
25x4 + -55x2 + 15 = 0

Reorder the terms:
15 + -55x2 + 25x4 = 0

Solving
15 + -55x2 + 25x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + -11x2 + 5x4) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(3 + -11x2 + 5x4)' equal to zero and attempt to solve:

Simplifying
3 + -11x2 + 5x4 = 0

Solving
3 + -11x2 + 5x4 = 0

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

Divide each side by '5'.
0.6 + -2.2x2 + x4 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -2.2x2 + -0.6 + x4 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -2.2x2 + x4 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -2.2x2 + x4 = 0 + -0.6
-2.2x2 + x4 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-2.2x2 + x4 = -0.6

The x term is -2.2x2.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x2 + 1.21 + x4 = -0.6 + 1.21

Reorder the terms:
1.21 + -2.2x2 + x4 = -0.6 + 1.21

Combine like terms: -0.6 + 1.21 = 0.61
1.21 + -2.2x2 + x4 = 0.61

Factor a perfect square on the left side:
(x2 + -1.1)(x2 + -1.1) = 0.61

Calculate the square root of the right side: 0.781024968

Break this problem into two subproblems by setting 
(x2 + -1.1) equal to 0.781024968 and -0.781024968.

Subproblem 1
x2 + -1.1 = 0.781024968

Simplifying
x2 + -1.1 = 0.781024968

Reorder the terms:
-1.1 + x2 = 0.781024968

Solving
-1.1 + x2 = 0.781024968

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x2 = 0.781024968 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x2 = 0.781024968 + 1.1
x2 = 0.781024968 + 1.1

Combine like terms: 0.781024968 + 1.1 = 1.881024968
x2 = 1.881024968

Simplifying
x2 = 1.881024968

Take the square root of each side:
x = {-1.371504637, 1.371504637}

Subproblem 2
x2 + -1.1 = -0.781024968

Simplifying
x2 + -1.1 = -0.781024968

Reorder the terms:
-1.1 + x2 = -0.781024968

Solving
-1.1 + x2 = -0.781024968

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x2 = -0.781024968 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x2 = -0.781024968 + 1.1
x2 = -0.781024968 + 1.1

Combine like terms: -0.781024968 + 1.1 = 0.318975032
x2 = 0.318975032

Simplifying
x2 = 0.318975032

Take the square root of each side:
x = {-0.564778746, 0.564778746}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.371504637, 1.371504637, -0.564778746, 0.564778746}
Solution
x = {-1.371504637, 1.371504637, -0.564778746, 0.564778746}