3x-0.01x^2=200

Solution for 3x-0.01x^2=200 equation:

Simplifying
3x + -0.01x2 = 200

Solving
3x + -0.01x2 = 200

Solving for variable 'x'.

Reorder the terms:
-200 + 3x + -0.01x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-200 + 3x + -0.01x2 = 0

Begin completing the square.  Divide all terms by
-0.01 the coefficient of the squared term: 

Divide each side by '-0.01'.
20000 + -300x + x2 = 0

Move the constant term to the right:

Add '-20000' to each side of the equation.
20000 + -300x + -20000 + x2 = 0 + -20000

Reorder the terms:
20000 + -20000 + -300x + x2 = 0 + -20000

Combine like terms: 20000 + -20000 = 0
0 + -300x + x2 = 0 + -20000
-300x + x2 = 0 + -20000

Combine like terms: 0 + -20000 = -20000
-300x + x2 = -20000

The x term is -300x.  Take half its coefficient (-150).
Square it (22500) and add it to both sides.

Add '22500' to each side of the equation.
-300x + 22500 + x2 = -20000 + 22500

Reorder the terms:
22500 + -300x + x2 = -20000 + 22500

Combine like terms: -20000 + 22500 = 2500
22500 + -300x + x2 = 2500

Factor a perfect square on the left side:
(x + -150)(x + -150) = 2500

Calculate the square root of the right side: 50

Break this problem into two subproblems by setting 
(x + -150) equal to 50 and -50.

Subproblem 1
x + -150 = 50

Simplifying
x + -150 = 50

Reorder the terms:
-150 + x = 50

Solving
-150 + x = 50

Solving for variable 'x'.

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

Add '150' to each side of the equation.
-150 + 150 + x = 50 + 150

Combine like terms: -150 + 150 = 0
0 + x = 50 + 150
x = 50 + 150

Combine like terms: 50 + 150 = 200
x = 200

Simplifying
x = 200

Subproblem 2
x + -150 = -50

Simplifying
x + -150 = -50

Reorder the terms:
-150 + x = -50

Solving
-150 + x = -50

Solving for variable 'x'.

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

Add '150' to each side of the equation.
-150 + 150 + x = -50 + 150

Combine like terms: -150 + 150 = 0
0 + x = -50 + 150
x = -50 + 150

Combine like terms: -50 + 150 = 100
x = 100

Simplifying
x = 100

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {200, 100}