x(1.8+x)=.19

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Solution for x(1.8+x)=.19 equation: 


Simplifying
x(1.8 + x) = 0.19
(1.8 * x + x * x) = 0.19
(1.8x + x2) = 0.19

Solving
1.8x + x2 = 0.19

Solving for variable 'x'.

Reorder the terms:
-0.19 + 1.8x + x2 = 0.19 + -0.19

Combine like terms: 0.19 + -0.19 = 0.00
-0.19 + 1.8x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.19' to each side of the equation.
-0.19 + 1.8x + 0.19 + x2 = 0.00 + 0.19

Reorder the terms:
-0.19 + 0.19 + 1.8x + x2 = 0.00 + 0.19

Combine like terms: -0.19 + 0.19 = 0.00
0.00 + 1.8x + x2 = 0.00 + 0.19
1.8x + x2 = 0.00 + 0.19

Combine like terms: 0.00 + 0.19 = 0.19
1.8x + x2 = 0.19

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 0.19 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 0.19 + 0.81

Combine like terms: 0.19 + 0.81 = 1
0.81 + 1.8x + x2 = 1

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.9) equal to 1 and -1.


Subproblem 1
x + 0.9 = 1

Simplifying
x + 0.9 = 1

Reorder the terms:
0.9 + x = 1

Solving
0.9 + x = 1

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 1 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 1 + -0.9
x = 1 + -0.9

Combine like terms: 1 + -0.9 = 0.1
x = 0.1

Simplifying
x = 0.1


Subproblem 2
x + 0.9 = -1

Simplifying
x + 0.9 = -1

Reorder the terms:
0.9 + x = -1

Solving
0.9 + x = -1

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -1 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -1 + -0.9
x = -1 + -0.9

Combine like terms: -1 + -0.9 = -1.9
x = -1.9

Simplifying
x = -1.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1, -1.9}

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