-x^2+200x-1600=0

Solution for -x^2+200x-1600=0 equation:

Simplifying
-1x2 + 200x + -1600 = 0

Reorder the terms:
-1600 + 200x + -1x2 = 0

Solving
-1600 + 200x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1600 + -200x + x2 = 0

Move the constant term to the right:

Add '-1600' to each side of the equation.
1600 + -200x + -1600 + x2 = 0 + -1600

Reorder the terms:
1600 + -1600 + -200x + x2 = 0 + -1600

Combine like terms: 1600 + -1600 = 0
0 + -200x + x2 = 0 + -1600
-200x + x2 = 0 + -1600

Combine like terms: 0 + -1600 = -1600
-200x + x2 = -1600

The x term is -200x.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200x + 10000 + x2 = -1600 + 10000

Reorder the terms:
10000 + -200x + x2 = -1600 + 10000

Combine like terms: -1600 + 10000 = 8400
10000 + -200x + x2 = 8400

Factor a perfect square on the left side:
(x + -100)(x + -100) = 8400

Calculate the square root of the right side: 91.651513899

Break this problem into two subproblems by setting 
(x + -100) equal to 91.651513899 and -91.651513899.

Subproblem 1
x + -100 = 91.651513899

Simplifying
x + -100 = 91.651513899

Reorder the terms:
-100 + x = 91.651513899

Solving
-100 + x = 91.651513899

Solving for variable 'x'.

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

Add '100' to each side of the equation.
-100 + 100 + x = 91.651513899 + 100

Combine like terms: -100 + 100 = 0
0 + x = 91.651513899 + 100
x = 91.651513899 + 100

Combine like terms: 91.651513899 + 100 = 191.651513899
x = 191.651513899

Simplifying
x = 191.651513899

Subproblem 2
x + -100 = -91.651513899

Simplifying
x + -100 = -91.651513899

Reorder the terms:
-100 + x = -91.651513899

Solving
-100 + x = -91.651513899

Solving for variable 'x'.

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

Add '100' to each side of the equation.
-100 + 100 + x = -91.651513899 + 100

Combine like terms: -100 + 100 = 0
0 + x = -91.651513899 + 100
x = -91.651513899 + 100

Combine like terms: -91.651513899 + 100 = 8.348486101
x = 8.348486101

Simplifying
x = 8.348486101

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {191.651513899, 8.348486101}