x^2=0.11-1.8x

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Solution for x^2=0.11-1.8x equation: 


Simplifying
x2 = 0.11 + -1.8x

Solving
x2 = 0.11 + -1.8x

Solving for variable 'x'.

Reorder the terms:
-0.11 + 1.8x + x2 = 0.11 + -1.8x + -0.11 + 1.8x

Reorder the terms:
-0.11 + 1.8x + x2 = 0.11 + -0.11 + -1.8x + 1.8x

Combine like terms: 0.11 + -0.11 = 0.00
-0.11 + 1.8x + x2 = 0.00 + -1.8x + 1.8x
-0.11 + 1.8x + x2 = -1.8x + 1.8x

Combine like terms: -1.8x + 1.8x = 0.0
-0.11 + 1.8x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.11' to each side of the equation.
-0.11 + 1.8x + 0.11 + x2 = 0.0 + 0.11

Reorder the terms:
-0.11 + 0.11 + 1.8x + x2 = 0.0 + 0.11

Combine like terms: -0.11 + 0.11 = 0.00
0.00 + 1.8x + x2 = 0.0 + 0.11
1.8x + x2 = 0.0 + 0.11

Combine like terms: 0.0 + 0.11 = 0.11
1.8x + x2 = 0.11

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 = 0.11 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 0.11 + 0.81

Combine like terms: 0.11 + 0.81 = 0.92
0.81 + 1.8x + x2 = 0.92

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 0.92

Calculate the square root of the right side: 0.959166305

Break this problem into two subproblems by setting 
(x + 0.9) equal to 0.959166305 and -0.959166305.


Subproblem 1
x + 0.9 = 0.959166305

Simplifying
x + 0.9 = 0.959166305

Reorder the terms:
0.9 + x = 0.959166305

Solving
0.9 + x = 0.959166305

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 = 0.959166305 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 0.959166305 + -0.9
x = 0.959166305 + -0.9

Combine like terms: 0.959166305 + -0.9 = 0.059166305
x = 0.059166305

Simplifying
x = 0.059166305


Subproblem 2
x + 0.9 = -0.959166305

Simplifying
x + 0.9 = -0.959166305

Reorder the terms:
0.9 + x = -0.959166305

Solving
0.9 + x = -0.959166305

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 = -0.959166305 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -0.959166305 + -0.9
x = -0.959166305 + -0.9

Combine like terms: -0.959166305 + -0.9 = -1.859166305
x = -1.859166305

Simplifying
x = -1.859166305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.059166305, -1.859166305}

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