22x^2-47x+20=0

Solution for 22x^2-47x+20=0 equation:

Simplifying
22x2 + -47x + 20 = 0

Reorder the terms:
20 + -47x + 22x2 = 0

Solving
20 + -47x + 22x2 = 0

Solving for variable 'x'.

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

Divide each side by '22'.
0.9090909091 + -2.136363636x + x2 = 0

Move the constant term to the right:

Add '-0.9090909091' to each side of the equation.
0.9090909091 + -2.136363636x + -0.9090909091 + x2 = 0 + -0.9090909091

Reorder the terms:
0.9090909091 + -0.9090909091 + -2.136363636x + x2 = 0 + -0.9090909091

Combine like terms: 0.9090909091 + -0.9090909091 = 0.0000000000
0.0000000000 + -2.136363636x + x2 = 0 + -0.9090909091
-2.136363636x + x2 = 0 + -0.9090909091

Combine like terms: 0 + -0.9090909091 = -0.9090909091
-2.136363636x + x2 = -0.9090909091

The x term is -2.136363636x.  Take half its coefficient (-1.068181818).
Square it (1.141012396) and add it to both sides.

Add '1.141012396' to each side of the equation.
-2.136363636x + 1.141012396 + x2 = -0.9090909091 + 1.141012396

Reorder the terms:
1.141012396 + -2.136363636x + x2 = -0.9090909091 + 1.141012396

Combine like terms: -0.9090909091 + 1.141012396 = 0.2319214869
1.141012396 + -2.136363636x + x2 = 0.2319214869

Factor a perfect square on the left side:
(x + -1.068181818)(x + -1.068181818) = 0.2319214869

Calculate the square root of the right side: 0.481582274

Break this problem into two subproblems by setting 
(x + -1.068181818) equal to 0.481582274 and -0.481582274.

Subproblem 1
x + -1.068181818 = 0.481582274

Simplifying
x + -1.068181818 = 0.481582274

Reorder the terms:
-1.068181818 + x = 0.481582274

Solving
-1.068181818 + x = 0.481582274

Solving for variable 'x'.

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

Add '1.068181818' to each side of the equation.
-1.068181818 + 1.068181818 + x = 0.481582274 + 1.068181818

Combine like terms: -1.068181818 + 1.068181818 = 0.000000000
0.000000000 + x = 0.481582274 + 1.068181818
x = 0.481582274 + 1.068181818

Combine like terms: 0.481582274 + 1.068181818 = 1.549764092
x = 1.549764092

Simplifying
x = 1.549764092

Subproblem 2
x + -1.068181818 = -0.481582274

Simplifying
x + -1.068181818 = -0.481582274

Reorder the terms:
-1.068181818 + x = -0.481582274

Solving
-1.068181818 + x = -0.481582274

Solving for variable 'x'.

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

Add '1.068181818' to each side of the equation.
-1.068181818 + 1.068181818 + x = -0.481582274 + 1.068181818

Combine like terms: -1.068181818 + 1.068181818 = 0.000000000
0.000000000 + x = -0.481582274 + 1.068181818
x = -0.481582274 + 1.068181818

Combine like terms: -0.481582274 + 1.068181818 = 0.586599544
x = 0.586599544

Simplifying
x = 0.586599544

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.549764092, 0.586599544}