-0.007x^2+0.877x-0.127=0

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Solution for -0.007x^2+0.877x-0.127=0 equation: 


Simplifying
-0.007x2 + 0.877x + -0.127 = 0

Reorder the terms:
-0.127 + 0.877x + -0.007x2 = 0

Solving
-0.127 + 0.877x + -0.007x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.007 the coefficient of the squared term: 

Divide each side by '-0.007'.
18.14285714 + -125.2857143x + x2 = 0

Move the constant term to the right:

Add '-18.14285714' to each side of the equation.
18.14285714 + -125.2857143x + -18.14285714 + x2 = 0 + -18.14285714

Reorder the terms:
18.14285714 + -18.14285714 + -125.2857143x + x2 = 0 + -18.14285714

Combine like terms: 18.14285714 + -18.14285714 = 0.00000000
0.00000000 + -125.2857143x + x2 = 0 + -18.14285714
-125.2857143x + x2 = 0 + -18.14285714

Combine like terms: 0 + -18.14285714 = -18.14285714
-125.2857143x + x2 = -18.14285714

The x term is -125.2857143x.  Take half its coefficient (-62.64285715).
Square it (3924.127552) and add it to both sides.

Add '3924.127552' to each side of the equation.
-125.2857143x + 3924.127552 + x2 = -18.14285714 + 3924.127552

Reorder the terms:
3924.127552 + -125.2857143x + x2 = -18.14285714 + 3924.127552

Combine like terms: -18.14285714 + 3924.127552 = 3905.98469486
3924.127552 + -125.2857143x + x2 = 3905.98469486

Factor a perfect square on the left side:
(x + -62.64285715)(x + -62.64285715) = 3905.98469486

Calculate the square root of the right side: 62.497877523

Break this problem into two subproblems by setting 
(x + -62.64285715) equal to 62.497877523 and -62.497877523.


Subproblem 1
x + -62.64285715 = 62.497877523

Simplifying
x + -62.64285715 = 62.497877523

Reorder the terms:
-62.64285715 + x = 62.497877523

Solving
-62.64285715 + x = 62.497877523

Solving for variable 'x'.

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

Add '62.64285715' to each side of the equation.
-62.64285715 + 62.64285715 + x = 62.497877523 + 62.64285715

Combine like terms: -62.64285715 + 62.64285715 = 0.00000000
0.00000000 + x = 62.497877523 + 62.64285715
x = 62.497877523 + 62.64285715

Combine like terms: 62.497877523 + 62.64285715 = 125.140734673
x = 125.140734673

Simplifying
x = 125.140734673


Subproblem 2
x + -62.64285715 = -62.497877523

Simplifying
x + -62.64285715 = -62.497877523

Reorder the terms:
-62.64285715 + x = -62.497877523

Solving
-62.64285715 + x = -62.497877523

Solving for variable 'x'.

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

Add '62.64285715' to each side of the equation.
-62.64285715 + 62.64285715 + x = -62.497877523 + 62.64285715

Combine like terms: -62.64285715 + 62.64285715 = 0.00000000
0.00000000 + x = -62.497877523 + 62.64285715
x = -62.497877523 + 62.64285715

Combine like terms: -62.497877523 + 62.64285715 = 0.144979627
x = 0.144979627

Simplifying
x = 0.144979627


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {125.140734673, 0.144979627}

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