0.567x(5.6+x)=(4-x)(4.4-x)

Solution for 0.567x(5.6+x)=(4-x)(4.4-x) equation:

Simplifying
0.567x(5.6 + x) = (4 + -1x)(4.4 + -1x)
(5.6 * 0.567x + x * 0.567x) = (4 + -1x)(4.4 + -1x)
(3.1752x + 0.567x2) = (4 + -1x)(4.4 + -1x)

Multiply (4 + -1x) * (4.4 + -1x)
3.1752x + 0.567x2 = (4(4.4 + -1x) + -1x * (4.4 + -1x))
3.1752x + 0.567x2 = ((4.4 * 4 + -1x * 4) + -1x * (4.4 + -1x))
3.1752x + 0.567x2 = ((17.6 + -4x) + -1x * (4.4 + -1x))
3.1752x + 0.567x2 = (17.6 + -4x + (4.4 * -1x + -1x * -1x))
3.1752x + 0.567x2 = (17.6 + -4x + (-4.4x + 1x2))

Combine like terms: -4x + -4.4x = -8.4x
3.1752x + 0.567x2 = (17.6 + -8.4x + 1x2)

Solving
3.1752x + 0.567x2 = 17.6 + -8.4x + 1x2

Solving for variable 'x'.

Reorder the terms:
-17.6 + 3.1752x + 8.4x + 0.567x2 + -1x2 = 17.6 + -8.4x + 1x2 + -17.6 + 8.4x + -1x2

Combine like terms: 3.1752x + 8.4x = 11.5752x
-17.6 + 11.5752x + 0.567x2 + -1x2 = 17.6 + -8.4x + 1x2 + -17.6 + 8.4x + -1x2

Combine like terms: 0.567x2 + -1x2 = -0.433x2
-17.6 + 11.5752x + -0.433x2 = 17.6 + -8.4x + 1x2 + -17.6 + 8.4x + -1x2

Reorder the terms:
-17.6 + 11.5752x + -0.433x2 = 17.6 + -17.6 + -8.4x + 8.4x + 1x2 + -1x2

Combine like terms: 17.6 + -17.6 = 0.0
-17.6 + 11.5752x + -0.433x2 = 0.0 + -8.4x + 8.4x + 1x2 + -1x2
-17.6 + 11.5752x + -0.433x2 = -8.4x + 8.4x + 1x2 + -1x2

Combine like terms: -8.4x + 8.4x = 0.0
-17.6 + 11.5752x + -0.433x2 = 0.0 + 1x2 + -1x2
-17.6 + 11.5752x + -0.433x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-17.6 + 11.5752x + -0.433x2 = 0

Begin completing the square.  Divide all terms by
-0.433 the coefficient of the squared term: 

Divide each side by '-0.433'.
40.64665127 + -26.73256351x + x2 = 0

Move the constant term to the right:

Add '-40.64665127' to each side of the equation.
40.64665127 + -26.73256351x + -40.64665127 + x2 = 0 + -40.64665127

Reorder the terms:
40.64665127 + -40.64665127 + -26.73256351x + x2 = 0 + -40.64665127

Combine like terms: 40.64665127 + -40.64665127 = 0.00000000
0.00000000 + -26.73256351x + x2 = 0 + -40.64665127
-26.73256351x + x2 = 0 + -40.64665127

Combine like terms: 0 + -40.64665127 = -40.64665127
-26.73256351x + x2 = -40.64665127

The x term is -26.73256351x.  Take half its coefficient (-13.36628176).
Square it (178.6574881) and add it to both sides.

Add '178.6574881' to each side of the equation.
-26.73256351x + 178.6574881 + x2 = -40.64665127 + 178.6574881

Reorder the terms:
178.6574881 + -26.73256351x + x2 = -40.64665127 + 178.6574881

Combine like terms: -40.64665127 + 178.6574881 = 138.01083683
178.6574881 + -26.73256351x + x2 = 138.01083683

Factor a perfect square on the left side:
(x + -13.36628176)(x + -13.36628176) = 138.01083683

Calculate the square root of the right side: 11.747801362

Break this problem into two subproblems by setting 
(x + -13.36628176) equal to 11.747801362 and -11.747801362.

Subproblem 1
x + -13.36628176 = 11.747801362

Simplifying
x + -13.36628176 = 11.747801362

Reorder the terms:
-13.36628176 + x = 11.747801362

Solving
-13.36628176 + x = 11.747801362

Solving for variable 'x'.

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

Add '13.36628176' to each side of the equation.
-13.36628176 + 13.36628176 + x = 11.747801362 + 13.36628176

Combine like terms: -13.36628176 + 13.36628176 = 0.00000000
0.00000000 + x = 11.747801362 + 13.36628176
x = 11.747801362 + 13.36628176

Combine like terms: 11.747801362 + 13.36628176 = 25.114083122
x = 25.114083122

Simplifying
x = 25.114083122

Subproblem 2
x + -13.36628176 = -11.747801362

Simplifying
x + -13.36628176 = -11.747801362

Reorder the terms:
-13.36628176 + x = -11.747801362

Solving
-13.36628176 + x = -11.747801362

Solving for variable 'x'.

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

Add '13.36628176' to each side of the equation.
-13.36628176 + 13.36628176 + x = -11.747801362 + 13.36628176

Combine like terms: -13.36628176 + 13.36628176 = 0.00000000
0.00000000 + x = -11.747801362 + 13.36628176
x = -11.747801362 + 13.36628176

Combine like terms: -11.747801362 + 13.36628176 = 1.618480398
x = 1.618480398

Simplifying
x = 1.618480398

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.114083122, 1.618480398}