-50=x-0.01x^2

Solution for -50=x-0.01x^2 equation:

Simplifying
-50 = x + -0.01x2

Solving
-50 = x + -0.01x2

Solving for variable 'x'.

Reorder the terms:
-50 + -1x + 0.01x2 = x + -1x + -0.01x2 + 0.01x2

Combine like terms: x + -1x = 0
-50 + -1x + 0.01x2 = 0 + -0.01x2 + 0.01x2
-50 + -1x + 0.01x2 = -0.01x2 + 0.01x2

Combine like terms: -0.01x2 + 0.01x2 = 0.00
-50 + -1x + 0.01x2 = 0.00

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

Divide each side by '0.01'.
-5000 + -100x + x2 = 0

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + -100x + 5000 + x2 = 0 + 5000

Reorder the terms:
-5000 + 5000 + -100x + x2 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + -100x + x2 = 0 + 5000
-100x + x2 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
-100x + x2 = 5000

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = 5000 + 2500

Reorder the terms:
2500 + -100x + x2 = 5000 + 2500

Combine like terms: 5000 + 2500 = 7500
2500 + -100x + x2 = 7500

Factor a perfect square on the left side:
(x + -50)(x + -50) = 7500

Calculate the square root of the right side: 86.602540378

Break this problem into two subproblems by setting 
(x + -50) equal to 86.602540378 and -86.602540378.

Subproblem 1
x + -50 = 86.602540378

Simplifying
x + -50 = 86.602540378

Reorder the terms:
-50 + x = 86.602540378

Solving
-50 + x = 86.602540378

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = 86.602540378 + 50

Combine like terms: -50 + 50 = 0
0 + x = 86.602540378 + 50
x = 86.602540378 + 50

Combine like terms: 86.602540378 + 50 = 136.602540378
x = 136.602540378

Simplifying
x = 136.602540378

Subproblem 2
x + -50 = -86.602540378

Simplifying
x + -50 = -86.602540378

Reorder the terms:
-50 + x = -86.602540378

Solving
-50 + x = -86.602540378

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = -86.602540378 + 50

Combine like terms: -50 + 50 = 0
0 + x = -86.602540378 + 50
x = -86.602540378 + 50

Combine like terms: -86.602540378 + 50 = -36.602540378
x = -36.602540378

Simplifying
x = -36.602540378

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {136.602540378, -36.602540378}