224x^5-404x^3+20x=0

Solution for 224x^5-404x^3+20x=0 equation:

Simplifying
224x5 + -404x3 + 20x = 0

Reorder the terms:
20x + -404x3 + 224x5 = 0

Solving
20x + -404x3 + 224x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(5 + -101x2 + 56x4) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(5 + -101x2 + 56x4)' equal to zero and attempt to solve:

Simplifying
5 + -101x2 + 56x4 = 0

Solving
5 + -101x2 + 56x4 = 0

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

Divide each side by '56'.
0.08928571429 + -1.803571429x2 + x4 = 0

Move the constant term to the right:

Add '-0.08928571429' to each side of the equation.
0.08928571429 + -1.803571429x2 + -0.08928571429 + x4 = 0 + -0.08928571429

Reorder the terms:
0.08928571429 + -0.08928571429 + -1.803571429x2 + x4 = 0 + -0.08928571429

Combine like terms: 0.08928571429 + -0.08928571429 = 0.00000000000
0.00000000000 + -1.803571429x2 + x4 = 0 + -0.08928571429
-1.803571429x2 + x4 = 0 + -0.08928571429

Combine like terms: 0 + -0.08928571429 = -0.08928571429
-1.803571429x2 + x4 = -0.08928571429

The x term is -1.803571429x2.  Take half its coefficient (-0.9017857145).
Square it (0.8132174749) and add it to both sides.

Add '0.8132174749' to each side of the equation.
-1.803571429x2 + 0.8132174749 + x4 = -0.08928571429 + 0.8132174749

Reorder the terms:
0.8132174749 + -1.803571429x2 + x4 = -0.08928571429 + 0.8132174749

Combine like terms: -0.08928571429 + 0.8132174749 = 0.72393176061
0.8132174749 + -1.803571429x2 + x4 = 0.72393176061

Factor a perfect square on the left side:
(x2 + -0.9017857145)(x2 + -0.9017857145) = 0.72393176061

Calculate the square root of the right side: 0.850841795

Break this problem into two subproblems by setting 
(x2 + -0.9017857145) equal to 0.850841795 and -0.850841795.

Subproblem 1
x2 + -0.9017857145 = 0.850841795

Simplifying
x2 + -0.9017857145 = 0.850841795

Reorder the terms:
-0.9017857145 + x2 = 0.850841795

Solving
-0.9017857145 + x2 = 0.850841795

Solving for variable 'x'.

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

Add '0.9017857145' to each side of the equation.
-0.9017857145 + 0.9017857145 + x2 = 0.850841795 + 0.9017857145

Combine like terms: -0.9017857145 + 0.9017857145 = 0.0000000000
0.0000000000 + x2 = 0.850841795 + 0.9017857145
x2 = 0.850841795 + 0.9017857145

Combine like terms: 0.850841795 + 0.9017857145 = 1.7526275095
x2 = 1.7526275095

Simplifying
x2 = 1.7526275095

Take the square root of each side:
x = {-1.323868388, 1.323868388}

Subproblem 2
x2 + -0.9017857145 = -0.850841795

Simplifying
x2 + -0.9017857145 = -0.850841795

Reorder the terms:
-0.9017857145 + x2 = -0.850841795

Solving
-0.9017857145 + x2 = -0.850841795

Solving for variable 'x'.

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

Add '0.9017857145' to each side of the equation.
-0.9017857145 + 0.9017857145 + x2 = -0.850841795 + 0.9017857145

Combine like terms: -0.9017857145 + 0.9017857145 = 0.0000000000
0.0000000000 + x2 = -0.850841795 + 0.9017857145
x2 = -0.850841795 + 0.9017857145

Combine like terms: -0.850841795 + 0.9017857145 = 0.0509439195
x2 = 0.0509439195

Simplifying
x2 = 0.0509439195

Take the square root of each side:
x = {-0.225707597, 0.225707597}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.323868388, 1.323868388, -0.225707597, 0.225707597}
Solution
x = {0, -1.323868388, 1.323868388, -0.225707597, 0.225707597}