-1000x^2+1100x-12.5=200

Solution for -1000x^2+1100x-12.5=200 equation:

Simplifying
-1000x2 + 1100x + -12.5 = 200

Reorder the terms:
-12.5 + 1100x + -1000x2 = 200

Solving
-12.5 + 1100x + -1000x2 = 200

Solving for variable 'x'.

Reorder the terms:
-12.5 + -200 + 1100x + -1000x2 = 200 + -200

Combine like terms: -12.5 + -200 = -212.5
-212.5 + 1100x + -1000x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-212.5 + 1100x + -1000x2 = 0

Begin completing the square.  Divide all terms by
-1000 the coefficient of the squared term: 

Divide each side by '-1000'.
0.2125 + -1.1x + x2 = 0

Move the constant term to the right:

Add '-0.2125' to each side of the equation.
0.2125 + -1.1x + -0.2125 + x2 = 0 + -0.2125

Reorder the terms:
0.2125 + -0.2125 + -1.1x + x2 = 0 + -0.2125

Combine like terms: 0.2125 + -0.2125 = 0.0000
0.0000 + -1.1x + x2 = 0 + -0.2125
-1.1x + x2 = 0 + -0.2125

Combine like terms: 0 + -0.2125 = -0.2125
-1.1x + x2 = -0.2125

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = -0.2125 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = -0.2125 + 0.3025

Combine like terms: -0.2125 + 0.3025 = 0.09
0.3025 + -1.1x + x2 = 0.09

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 0.09

Calculate the square root of the right side: 0.3

Break this problem into two subproblems by setting 
(x + -0.55) equal to 0.3 and -0.3.

Subproblem 1
x + -0.55 = 0.3

Simplifying
x + -0.55 = 0.3

Reorder the terms:
-0.55 + x = 0.3

Solving
-0.55 + x = 0.3

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = 0.3 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = 0.3 + 0.55
x = 0.3 + 0.55

Combine like terms: 0.3 + 0.55 = 0.85
x = 0.85

Simplifying
x = 0.85

Subproblem 2
x + -0.55 = -0.3

Simplifying
x + -0.55 = -0.3

Reorder the terms:
-0.55 + x = -0.3

Solving
-0.55 + x = -0.3

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = -0.3 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = -0.3 + 0.55
x = -0.3 + 0.55

Combine like terms: -0.3 + 0.55 = 0.25
x = 0.25

Simplifying
x = 0.25

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.85, 0.25}