1200=x(600-x)

Solution for 1200=x(600-x) equation:

Simplifying
1200 = x(600 + -1x)
1200 = (600 * x + -1x * x)
1200 = (600x + -1x2)

Solving
1200 = 600x + -1x2

Solving for variable 'x'.

Reorder the terms:
1200 + -600x + x2 = 600x + -600x + -1x2 + x2

Combine like terms: 600x + -600x = 0
1200 + -600x + x2 = 0 + -1x2 + x2
1200 + -600x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1200 + -600x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1200' to each side of the equation.
1200 + -600x + -1200 + x2 = 0 + -1200

Reorder the terms:
1200 + -1200 + -600x + x2 = 0 + -1200

Combine like terms: 1200 + -1200 = 0
0 + -600x + x2 = 0 + -1200
-600x + x2 = 0 + -1200

Combine like terms: 0 + -1200 = -1200
-600x + x2 = -1200

The x term is -600x.  Take half its coefficient (-300).
Square it (90000) and add it to both sides.

Add '90000' to each side of the equation.
-600x + 90000 + x2 = -1200 + 90000

Reorder the terms:
90000 + -600x + x2 = -1200 + 90000

Combine like terms: -1200 + 90000 = 88800
90000 + -600x + x2 = 88800

Factor a perfect square on the left side:
(x + -300)(x + -300) = 88800

Calculate the square root of the right side: 297.993288515

Break this problem into two subproblems by setting 
(x + -300) equal to 297.993288515 and -297.993288515.

Subproblem 1
x + -300 = 297.993288515

Simplifying
x + -300 = 297.993288515

Reorder the terms:
-300 + x = 297.993288515

Solving
-300 + x = 297.993288515

Solving for variable 'x'.

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

Add '300' to each side of the equation.
-300 + 300 + x = 297.993288515 + 300

Combine like terms: -300 + 300 = 0
0 + x = 297.993288515 + 300
x = 297.993288515 + 300

Combine like terms: 297.993288515 + 300 = 597.993288515
x = 597.993288515

Simplifying
x = 597.993288515

Subproblem 2
x + -300 = -297.993288515

Simplifying
x + -300 = -297.993288515

Reorder the terms:
-300 + x = -297.993288515

Solving
-300 + x = -297.993288515

Solving for variable 'x'.

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

Add '300' to each side of the equation.
-300 + 300 + x = -297.993288515 + 300

Combine like terms: -300 + 300 = 0
0 + x = -297.993288515 + 300
x = -297.993288515 + 300

Combine like terms: -297.993288515 + 300 = 2.006711485
x = 2.006711485

Simplifying
x = 2.006711485

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {597.993288515, 2.006711485}