x(170-2x)=2800

Solution for x(170-2x)=2800 equation:

Simplifying
x(170 + -2x) = 2800
(170 * x + -2x * x) = 2800
(170x + -2x2) = 2800

Solving
170x + -2x2 = 2800

Solving for variable 'x'.

Reorder the terms:
-2800 + 170x + -2x2 = 2800 + -2800

Combine like terms: 2800 + -2800 = 0
-2800 + 170x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1400 + 85x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1400 + 85x + -1x2)' equal to zero and attempt to solve:

Simplifying
-1400 + 85x + -1x2 = 0

Solving
-1400 + 85x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1400 + -85x + x2 = 0

Move the constant term to the right:

Add '-1400' to each side of the equation.
1400 + -85x + -1400 + x2 = 0 + -1400

Reorder the terms:
1400 + -1400 + -85x + x2 = 0 + -1400

Combine like terms: 1400 + -1400 = 0
0 + -85x + x2 = 0 + -1400
-85x + x2 = 0 + -1400

Combine like terms: 0 + -1400 = -1400
-85x + x2 = -1400

The x term is -85x.  Take half its coefficient (-42.5).
Square it (1806.25) and add it to both sides.

Add '1806.25' to each side of the equation.
-85x + 1806.25 + x2 = -1400 + 1806.25

Reorder the terms:
1806.25 + -85x + x2 = -1400 + 1806.25

Combine like terms: -1400 + 1806.25 = 406.25
1806.25 + -85x + x2 = 406.25

Factor a perfect square on the left side:
(x + -42.5)(x + -42.5) = 406.25

Calculate the square root of the right side: 20.155644371

Break this problem into two subproblems by setting 
(x + -42.5) equal to 20.155644371 and -20.155644371.

Subproblem 1
x + -42.5 = 20.155644371

Simplifying
x + -42.5 = 20.155644371

Reorder the terms:
-42.5 + x = 20.155644371

Solving
-42.5 + x = 20.155644371

Solving for variable 'x'.

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

Add '42.5' to each side of the equation.
-42.5 + 42.5 + x = 20.155644371 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + x = 20.155644371 + 42.5
x = 20.155644371 + 42.5

Combine like terms: 20.155644371 + 42.5 = 62.655644371
x = 62.655644371

Simplifying
x = 62.655644371

Subproblem 2
x + -42.5 = -20.155644371

Simplifying
x + -42.5 = -20.155644371

Reorder the terms:
-42.5 + x = -20.155644371

Solving
-42.5 + x = -20.155644371

Solving for variable 'x'.

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

Add '42.5' to each side of the equation.
-42.5 + 42.5 + x = -20.155644371 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + x = -20.155644371 + 42.5
x = -20.155644371 + 42.5

Combine like terms: -20.155644371 + 42.5 = 22.344355629
x = 22.344355629

Simplifying
x = 22.344355629

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {62.655644371, 22.344355629}
Solution
x = {62.655644371, 22.344355629}