-.006x^2-.107x-.194=0

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Solution for -.006x^2-.107x-.194=0 equation: 


Simplifying
-0.006x2 + -0.107x + -0.194 = 0

Reorder the terms:
-0.194 + -0.107x + -0.006x2 = 0

Solving
-0.194 + -0.107x + -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'.
32.33333333 + 17.83333333x + x2 = 0

Move the constant term to the right:

Add '-32.33333333' to each side of the equation.
32.33333333 + 17.83333333x + -32.33333333 + x2 = 0 + -32.33333333

Reorder the terms:
32.33333333 + -32.33333333 + 17.83333333x + x2 = 0 + -32.33333333

Combine like terms: 32.33333333 + -32.33333333 = 0.00000000
0.00000000 + 17.83333333x + x2 = 0 + -32.33333333
17.83333333x + x2 = 0 + -32.33333333

Combine like terms: 0 + -32.33333333 = -32.33333333
17.83333333x + x2 = -32.33333333

The x term is 17.83333333x.  Take half its coefficient (8.916666665).
Square it (79.50694441) and add it to both sides.

Add '79.50694441' to each side of the equation.
17.83333333x + 79.50694441 + x2 = -32.33333333 + 79.50694441

Reorder the terms:
79.50694441 + 17.83333333x + x2 = -32.33333333 + 79.50694441

Combine like terms: -32.33333333 + 79.50694441 = 47.17361108
79.50694441 + 17.83333333x + x2 = 47.17361108

Factor a perfect square on the left side:
(x + 8.916666665)(x + 8.916666665) = 47.17361108

Calculate the square root of the right side: 6.868304819

Break this problem into two subproblems by setting 
(x + 8.916666665) equal to 6.868304819 and -6.868304819.


Subproblem 1
x + 8.916666665 = 6.868304819

Simplifying
x + 8.916666665 = 6.868304819

Reorder the terms:
8.916666665 + x = 6.868304819

Solving
8.916666665 + x = 6.868304819

Solving for variable 'x'.

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

Add '-8.916666665' to each side of the equation.
8.916666665 + -8.916666665 + x = 6.868304819 + -8.916666665

Combine like terms: 8.916666665 + -8.916666665 = 0.000000000
0.000000000 + x = 6.868304819 + -8.916666665
x = 6.868304819 + -8.916666665

Combine like terms: 6.868304819 + -8.916666665 = -2.048361846
x = -2.048361846

Simplifying
x = -2.048361846


Subproblem 2
x + 8.916666665 = -6.868304819

Simplifying
x + 8.916666665 = -6.868304819

Reorder the terms:
8.916666665 + x = -6.868304819

Solving
8.916666665 + x = -6.868304819

Solving for variable 'x'.

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

Add '-8.916666665' to each side of the equation.
8.916666665 + -8.916666665 + x = -6.868304819 + -8.916666665

Combine like terms: 8.916666665 + -8.916666665 = 0.000000000
0.000000000 + x = -6.868304819 + -8.916666665
x = -6.868304819 + -8.916666665

Combine like terms: -6.868304819 + -8.916666665 = -15.784971484
x = -15.784971484

Simplifying
x = -15.784971484


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.048361846, -15.784971484}

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