-0.009x^2+0.109x-0.195=0

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Solution for -0.009x^2+0.109x-0.195=0 equation: 


Simplifying
-0.009x2 + 0.109x + -0.195 = 0

Reorder the terms:
-0.195 + 0.109x + -0.009x2 = 0

Solving
-0.195 + 0.109x + -0.009x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.009 the coefficient of the squared term: 

Divide each side by '-0.009'.
21.66666667 + -12.11111111x + x2 = 0

Move the constant term to the right:

Add '-21.66666667' to each side of the equation.
21.66666667 + -12.11111111x + -21.66666667 + x2 = 0 + -21.66666667

Reorder the terms:
21.66666667 + -21.66666667 + -12.11111111x + x2 = 0 + -21.66666667

Combine like terms: 21.66666667 + -21.66666667 = 0.00000000
0.00000000 + -12.11111111x + x2 = 0 + -21.66666667
-12.11111111x + x2 = 0 + -21.66666667

Combine like terms: 0 + -21.66666667 = -21.66666667
-12.11111111x + x2 = -21.66666667

The x term is -12.11111111x.  Take half its coefficient (-6.055555555).
Square it (36.66975308) and add it to both sides.

Add '36.66975308' to each side of the equation.
-12.11111111x + 36.66975308 + x2 = -21.66666667 + 36.66975308

Reorder the terms:
36.66975308 + -12.11111111x + x2 = -21.66666667 + 36.66975308

Combine like terms: -21.66666667 + 36.66975308 = 15.00308641
36.66975308 + -12.11111111x + x2 = 15.00308641

Factor a perfect square on the left side:
(x + -6.055555555)(x + -6.055555555) = 15.00308641

Calculate the square root of the right side: 3.87338178

Break this problem into two subproblems by setting 
(x + -6.055555555) equal to 3.87338178 and -3.87338178.


Subproblem 1
x + -6.055555555 = 3.87338178

Simplifying
x + -6.055555555 = 3.87338178

Reorder the terms:
-6.055555555 + x = 3.87338178

Solving
-6.055555555 + x = 3.87338178

Solving for variable 'x'.

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

Add '6.055555555' to each side of the equation.
-6.055555555 + 6.055555555 + x = 3.87338178 + 6.055555555

Combine like terms: -6.055555555 + 6.055555555 = 0.000000000
0.000000000 + x = 3.87338178 + 6.055555555
x = 3.87338178 + 6.055555555

Combine like terms: 3.87338178 + 6.055555555 = 9.928937335
x = 9.928937335

Simplifying
x = 9.928937335


Subproblem 2
x + -6.055555555 = -3.87338178

Simplifying
x + -6.055555555 = -3.87338178

Reorder the terms:
-6.055555555 + x = -3.87338178

Solving
-6.055555555 + x = -3.87338178

Solving for variable 'x'.

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

Add '6.055555555' to each side of the equation.
-6.055555555 + 6.055555555 + x = -3.87338178 + 6.055555555

Combine like terms: -6.055555555 + 6.055555555 = 0.000000000
0.000000000 + x = -3.87338178 + 6.055555555
x = -3.87338178 + 6.055555555

Combine like terms: -3.87338178 + 6.055555555 = 2.182173775
x = 2.182173775

Simplifying
x = 2.182173775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.928937335, 2.182173775}

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