x+0.80(2)=0.90x(x+2)

Solution for x+0.80(2)=0.90x(x+2) equation:

Simplifying
x + 0.80(2) = 0.90x(x + 2)

Multiply 0.80 * 2
x + 1.6 = 0.90x(x + 2)

Reorder the terms:
1.6 + x = 0.90x(x + 2)

Reorder the terms:
1.6 + x = 0.90x(2 + x)
1.6 + x = (2 * 0.90x + x * 0.90x)
1.6 + x = (1.8x + 0.90x2)

Solving
1.6 + x = 1.8x + 0.90x2

Solving for variable 'x'.

Combine like terms: x + -1.8x = -0.8x
1.6 + -0.8x + -0.90x2 = 1.8x + 0.90x2 + -1.8x + -0.90x2

Reorder the terms:
1.6 + -0.8x + -0.90x2 = 1.8x + -1.8x + 0.90x2 + -0.90x2

Combine like terms: 1.8x + -1.8x = 0.0
1.6 + -0.8x + -0.90x2 = 0.0 + 0.90x2 + -0.90x2
1.6 + -0.8x + -0.90x2 = 0.90x2 + -0.90x2

Combine like terms: 0.90x2 + -0.90x2 = 0.00
1.6 + -0.8x + -0.90x2 = 0.00

Begin completing the square.  Divide all terms by
-0.90 the coefficient of the squared term: 

Divide each side by '-0.90'.
-1.777777778 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + 0.8888888889x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + 0.8888888889x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + 0.8888888889x + x2 = 0 + 1.777777778
0.8888888889x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
0.8888888889x + x2 = 1.777777778

The x term is 0.8888888889x.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889x + 0.1975308642 + x2 = 1.777777778 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = 1.777777778 + 0.1975308642

Combine like terms: 1.777777778 + 0.1975308642 = 1.9753086422
0.1975308642 + 0.8888888889x + x2 = 1.9753086422

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 1.9753086422

Calculate the square root of the right side: 1.405456738

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 1.405456738 and -1.405456738.

Subproblem 1
x + 0.4444444445 = 1.405456738

Simplifying
x + 0.4444444445 = 1.405456738

Reorder the terms:
0.4444444445 + x = 1.405456738

Solving
0.4444444445 + x = 1.405456738

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = 1.405456738 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = 1.405456738 + -0.4444444445
x = 1.405456738 + -0.4444444445

Combine like terms: 1.405456738 + -0.4444444445 = 0.9610122935
x = 0.9610122935

Simplifying
x = 0.9610122935

Subproblem 2
x + 0.4444444445 = -1.405456738

Simplifying
x + 0.4444444445 = -1.405456738

Reorder the terms:
0.4444444445 + x = -1.405456738

Solving
0.4444444445 + x = -1.405456738

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = -1.405456738 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = -1.405456738 + -0.4444444445
x = -1.405456738 + -0.4444444445

Combine like terms: -1.405456738 + -0.4444444445 = -1.8499011825
x = -1.8499011825

Simplifying
x = -1.8499011825

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9610122935, -1.8499011825}