25x-10x(11-x)=170

Solution for 25x-10x(11-x)=170 equation:

Simplifying
25x + -10x(11 + -1x) = 170
25x + (11 * -10x + -1x * -10x) = 170
25x + (-110x + 10x2) = 170

Combine like terms: 25x + -110x = -85x
-85x + 10x2 = 170

Solving
-85x + 10x2 = 170

Solving for variable 'x'.

Reorder the terms:
-170 + -85x + 10x2 = 170 + -170

Combine like terms: 170 + -170 = 0
-170 + -85x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-34 + -17x + 2x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-34 + -17x + 2x2)' equal to zero and attempt to solve:

Simplifying
-34 + -17x + 2x2 = 0

Solving
-34 + -17x + 2x2 = 0

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

Divide each side by '2'.
-17 + -8.5x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -8.5x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -8.5x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -8.5x + x2 = 0 + 17
-8.5x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-8.5x + x2 = 17

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = 17 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = 17 + 18.0625

Combine like terms: 17 + 18.0625 = 35.0625
18.0625 + -8.5x + x2 = 35.0625

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 35.0625

Calculate the square root of the right side: 5.921359641

Break this problem into two subproblems by setting 
(x + -4.25) equal to 5.921359641 and -5.921359641.

Subproblem 1
x + -4.25 = 5.921359641

Simplifying
x + -4.25 = 5.921359641

Reorder the terms:
-4.25 + x = 5.921359641

Solving
-4.25 + x = 5.921359641

Solving for variable 'x'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = 5.921359641 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = 5.921359641 + 4.25
x = 5.921359641 + 4.25

Combine like terms: 5.921359641 + 4.25 = 10.171359641
x = 10.171359641

Simplifying
x = 10.171359641

Subproblem 2
x + -4.25 = -5.921359641

Simplifying
x + -4.25 = -5.921359641

Reorder the terms:
-4.25 + x = -5.921359641

Solving
-4.25 + x = -5.921359641

Solving for variable 'x'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = -5.921359641 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = -5.921359641 + 4.25
x = -5.921359641 + 4.25

Combine like terms: -5.921359641 + 4.25 = -1.671359641
x = -1.671359641

Simplifying
x = -1.671359641

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.171359641, -1.671359641}
Solution
x = {10.171359641, -1.671359641}