-0.006x^2+0.101x-0.193=0

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Solution for -0.006x^2+0.101x-0.193=0 equation: 


Simplifying
-0.006x2 + 0.101x + -0.193 = 0

Reorder the terms:
-0.193 + 0.101x + -0.006x2 = 0

Solving
-0.193 + 0.101x + -0.006x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.006 the coefficient of the squared term: 

Divide each side by '-0.006'.
32.16666667 + -16.83333333x + x2 = 0

Move the constant term to the right:

Add '-32.16666667' to each side of the equation.
32.16666667 + -16.83333333x + -32.16666667 + x2 = 0 + -32.16666667

Reorder the terms:
32.16666667 + -32.16666667 + -16.83333333x + x2 = 0 + -32.16666667

Combine like terms: 32.16666667 + -32.16666667 = 0.00000000
0.00000000 + -16.83333333x + x2 = 0 + -32.16666667
-16.83333333x + x2 = 0 + -32.16666667

Combine like terms: 0 + -32.16666667 = -32.16666667
-16.83333333x + x2 = -32.16666667

The x term is -16.83333333x.  Take half its coefficient (-8.416666665).
Square it (70.84027775) and add it to both sides.

Add '70.84027775' to each side of the equation.
-16.83333333x + 70.84027775 + x2 = -32.16666667 + 70.84027775

Reorder the terms:
70.84027775 + -16.83333333x + x2 = -32.16666667 + 70.84027775

Combine like terms: -32.16666667 + 70.84027775 = 38.67361108
70.84027775 + -16.83333333x + x2 = 38.67361108

Factor a perfect square on the left side:
(x + -8.416666665)(x + -8.416666665) = 38.67361108

Calculate the square root of the right side: 6.218811066

Break this problem into two subproblems by setting 
(x + -8.416666665) equal to 6.218811066 and -6.218811066.


Subproblem 1
x + -8.416666665 = 6.218811066

Simplifying
x + -8.416666665 = 6.218811066

Reorder the terms:
-8.416666665 + x = 6.218811066

Solving
-8.416666665 + x = 6.218811066

Solving for variable 'x'.

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

Add '8.416666665' to each side of the equation.
-8.416666665 + 8.416666665 + x = 6.218811066 + 8.416666665

Combine like terms: -8.416666665 + 8.416666665 = 0.000000000
0.000000000 + x = 6.218811066 + 8.416666665
x = 6.218811066 + 8.416666665

Combine like terms: 6.218811066 + 8.416666665 = 14.635477731
x = 14.635477731

Simplifying
x = 14.635477731


Subproblem 2
x + -8.416666665 = -6.218811066

Simplifying
x + -8.416666665 = -6.218811066

Reorder the terms:
-8.416666665 + x = -6.218811066

Solving
-8.416666665 + x = -6.218811066

Solving for variable 'x'.

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

Add '8.416666665' to each side of the equation.
-8.416666665 + 8.416666665 + x = -6.218811066 + 8.416666665

Combine like terms: -8.416666665 + 8.416666665 = 0.000000000
0.000000000 + x = -6.218811066 + 8.416666665
x = -6.218811066 + 8.416666665

Combine like terms: -6.218811066 + 8.416666665 = 2.197855599
x = 2.197855599

Simplifying
x = 2.197855599


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.635477731, 2.197855599}

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