15000=273x-x^2

Solution for 15000=273x-x^2 equation:

Simplifying
15000 = 273x + -1x2

Solving
15000 = 273x + -1x2

Solving for variable 'x'.

Reorder the terms:
15000 + -273x + x2 = 273x + -273x + -1x2 + x2

Combine like terms: 273x + -273x = 0
15000 + -273x + x2 = 0 + -1x2 + x2
15000 + -273x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
15000 + -273x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15000' to each side of the equation.
15000 + -273x + -15000 + x2 = 0 + -15000

Reorder the terms:
15000 + -15000 + -273x + x2 = 0 + -15000

Combine like terms: 15000 + -15000 = 0
0 + -273x + x2 = 0 + -15000
-273x + x2 = 0 + -15000

Combine like terms: 0 + -15000 = -15000
-273x + x2 = -15000

The x term is -273x.  Take half its coefficient (-136.5).
Square it (18632.25) and add it to both sides.

Add '18632.25' to each side of the equation.
-273x + 18632.25 + x2 = -15000 + 18632.25

Reorder the terms:
18632.25 + -273x + x2 = -15000 + 18632.25

Combine like terms: -15000 + 18632.25 = 3632.25
18632.25 + -273x + x2 = 3632.25

Factor a perfect square on the left side:
(x + -136.5)(x + -136.5) = 3632.25

Calculate the square root of the right side: 60.268150793

Break this problem into two subproblems by setting 
(x + -136.5) equal to 60.268150793 and -60.268150793.

Subproblem 1
x + -136.5 = 60.268150793

Simplifying
x + -136.5 = 60.268150793

Reorder the terms:
-136.5 + x = 60.268150793

Solving
-136.5 + x = 60.268150793

Solving for variable 'x'.

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

Add '136.5' to each side of the equation.
-136.5 + 136.5 + x = 60.268150793 + 136.5

Combine like terms: -136.5 + 136.5 = 0.0
0.0 + x = 60.268150793 + 136.5
x = 60.268150793 + 136.5

Combine like terms: 60.268150793 + 136.5 = 196.768150793
x = 196.768150793

Simplifying
x = 196.768150793

Subproblem 2
x + -136.5 = -60.268150793

Simplifying
x + -136.5 = -60.268150793

Reorder the terms:
-136.5 + x = -60.268150793

Solving
-136.5 + x = -60.268150793

Solving for variable 'x'.

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

Add '136.5' to each side of the equation.
-136.5 + 136.5 + x = -60.268150793 + 136.5

Combine like terms: -136.5 + 136.5 = 0.0
0.0 + x = -60.268150793 + 136.5
x = -60.268150793 + 136.5

Combine like terms: -60.268150793 + 136.5 = 76.231849207
x = 76.231849207

Simplifying
x = 76.231849207

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {196.768150793, 76.231849207}