200=-1000x^2+1100x

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

Simplifying
200 = -1000x2 + 1100x

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

Solving
200 = 1100x + -1000x2

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '100'.
100(2 + -11x + 10x2) = 0

Ignore the factor 100.
Subproblem 1
Set the factor '(2 + -11x + 10x2)' equal to zero and attempt to solve:

Simplifying
2 + -11x + 10x2 = 0

Solving
2 + -11x + 10x2 = 0

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

Divide each side by '10'.
0.2 + -1.1x + x2 = 0.0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.1x + -0.2 + x2 = 0.0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.1x + x2 = 0.0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.1x + x2 = 0.0 + -0.2
-1.1x + x2 = 0.0 + -0.2

Combine like terms: 0.0 + -0.2 = -0.2
-1.1x + x2 = -0.2

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 = -0.2 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = -0.2 + 0.3025

Combine like terms: -0.2 + 0.3025 = 0.1025
0.3025 + -1.1x + x2 = 0.1025

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 0.1025

Calculate the square root of the right side: 0.320156212

Break this problem into two subproblems by setting 
(x + -0.55) equal to 0.320156212 and -0.320156212.

Subproblem 1
x + -0.55 = 0.320156212

Simplifying
x + -0.55 = 0.320156212

Reorder the terms:
-0.55 + x = 0.320156212

Solving
-0.55 + x = 0.320156212

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 = 0.320156212 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = 0.320156212 + 0.55
x = 0.320156212 + 0.55

Combine like terms: 0.320156212 + 0.55 = 0.870156212
x = 0.870156212

Simplifying
x = 0.870156212

Subproblem 2
x + -0.55 = -0.320156212

Simplifying
x + -0.55 = -0.320156212

Reorder the terms:
-0.55 + x = -0.320156212

Solving
-0.55 + x = -0.320156212

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 = -0.320156212 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = -0.320156212 + 0.55
x = -0.320156212 + 0.55

Combine like terms: -0.320156212 + 0.55 = 0.229843788
x = 0.229843788

Simplifying
x = 0.229843788

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.870156212, 0.229843788}
Solution
x = {0.870156212, 0.229843788}