0=20x^2-44x+4

Solution for 0=20x^2-44x+4 equation:

Simplifying
0 = 20x2 + -44x + 4

Reorder the terms:
0 = 4 + -44x + 20x2

Solving
0 = 4 + -44x + 20x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + 44x + -20x2 = 4 + -44x + 20x2 + -4 + 44x + -20x2

Reorder the terms:
-4 + 44x + -20x2 = 4 + -4 + -44x + 44x + 20x2 + -20x2

Combine like terms: 4 + -4 = 0
-4 + 44x + -20x2 = 0 + -44x + 44x + 20x2 + -20x2
-4 + 44x + -20x2 = -44x + 44x + 20x2 + -20x2

Combine like terms: -44x + 44x = 0
-4 + 44x + -20x2 = 0 + 20x2 + -20x2
-4 + 44x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-4 + 44x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 11x + -5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 11x + -5x2)' equal to zero and attempt to solve:

Simplifying
-1 + 11x + -5x2 = 0

Solving
-1 + 11x + -5x2 = 0

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

Divide each side by '-5'.
0.2 + -2.2x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -2.2x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -2.2x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -2.2x + x2 = 0 + -0.2
-2.2x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-2.2x + x2 = -0.2

The x term is -2.2x.  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.
-2.2x + 1.21 + x2 = -0.2 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = -0.2 + 1.21

Combine like terms: -0.2 + 1.21 = 1.01
1.21 + -2.2x + x2 = 1.01

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 1.01

Calculate the square root of the right side: 1.004987562

Break this problem into two subproblems by setting 
(x + -1.1) equal to 1.004987562 and -1.004987562.

Subproblem 1
x + -1.1 = 1.004987562

Simplifying
x + -1.1 = 1.004987562

Reorder the terms:
-1.1 + x = 1.004987562

Solving
-1.1 + x = 1.004987562

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 + x = 1.004987562 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = 1.004987562 + 1.1
x = 1.004987562 + 1.1

Combine like terms: 1.004987562 + 1.1 = 2.104987562
x = 2.104987562

Simplifying
x = 2.104987562

Subproblem 2
x + -1.1 = -1.004987562

Simplifying
x + -1.1 = -1.004987562

Reorder the terms:
-1.1 + x = -1.004987562

Solving
-1.1 + x = -1.004987562

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 + x = -1.004987562 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = -1.004987562 + 1.1
x = -1.004987562 + 1.1

Combine like terms: -1.004987562 + 1.1 = 0.095012438
x = 0.095012438

Simplifying
x = 0.095012438

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.104987562, 0.095012438}
Solution
x = {2.104987562, 0.095012438}