600=600x-2x^2

Solution for 600=600x-2x^2 equation:

Simplifying
600 = 600x + -2x2

Solving
600 = 600x + -2x2

Solving for variable 'x'.

Reorder the terms:
600 + -600x + 2x2 = 600x + -600x + -2x2 + 2x2

Combine like terms: 600x + -600x = 0
600 + -600x + 2x2 = 0 + -2x2 + 2x2
600 + -600x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
600 + -600x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(300 + -300x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(300 + -300x + x2)' equal to zero and attempt to solve:

Simplifying
300 + -300x + x2 = 0

Solving
300 + -300x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -300 + 22500

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

Combine like terms: -300 + 22500 = 22200
22500 + -300x + x2 = 22200

Factor a perfect square on the left side:
(x + -150)(x + -150) = 22200

Calculate the square root of the right side: 148.996644258

Break this problem into two subproblems by setting 
(x + -150) equal to 148.996644258 and -148.996644258.

Subproblem 1
x + -150 = 148.996644258

Simplifying
x + -150 = 148.996644258

Reorder the terms:
-150 + x = 148.996644258

Solving
-150 + x = 148.996644258

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 = 148.996644258 + 150

Combine like terms: -150 + 150 = 0
0 + x = 148.996644258 + 150
x = 148.996644258 + 150

Combine like terms: 148.996644258 + 150 = 298.996644258
x = 298.996644258

Simplifying
x = 298.996644258

Subproblem 2
x + -150 = -148.996644258

Simplifying
x + -150 = -148.996644258

Reorder the terms:
-150 + x = -148.996644258

Solving
-150 + x = -148.996644258

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 = -148.996644258 + 150

Combine like terms: -150 + 150 = 0
0 + x = -148.996644258 + 150
x = -148.996644258 + 150

Combine like terms: -148.996644258 + 150 = 1.003355742
x = 1.003355742

Simplifying
x = 1.003355742

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {298.996644258, 1.003355742}
Solution
x = {298.996644258, 1.003355742}