8x-x(x-5)=x+25

Solution for 8x-x(x-5)=x+25 equation:

Simplifying
8x + -1x(x + -5) = x + 25

Reorder the terms:
8x + -1x(-5 + x) = x + 25
8x + (-5 * -1x + x * -1x) = x + 25
8x + (5x + -1x2) = x + 25

Combine like terms: 8x + 5x = 13x
13x + -1x2 = x + 25

Reorder the terms:
13x + -1x2 = 25 + x

Solving
13x + -1x2 = 25 + x

Solving for variable 'x'.

Reorder the terms:
-25 + 13x + -1x + -1x2 = 25 + x + -25 + -1x

Combine like terms: 13x + -1x = 12x
-25 + 12x + -1x2 = 25 + x + -25 + -1x

Reorder the terms:
-25 + 12x + -1x2 = 25 + -25 + x + -1x

Combine like terms: 25 + -25 = 0
-25 + 12x + -1x2 = 0 + x + -1x
-25 + 12x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
-25 + 12x + -1x2 = 0

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

Divide each side by '-1'.
25 + -12x + x2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -12x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -12x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -12x + x2 = 0 + -25
-12x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-12x + x2 = -25

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -25 + 36

Reorder the terms:
36 + -12x + x2 = -25 + 36

Combine like terms: -25 + 36 = 11
36 + -12x + x2 = 11

Factor a perfect square on the left side:
(x + -6)(x + -6) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -6) equal to 3.31662479 and -3.31662479.

Subproblem 1
x + -6 = 3.31662479

Simplifying
x + -6 = 3.31662479

Reorder the terms:
-6 + x = 3.31662479

Solving
-6 + x = 3.31662479

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 3.31662479 + 6

Combine like terms: -6 + 6 = 0
0 + x = 3.31662479 + 6
x = 3.31662479 + 6

Combine like terms: 3.31662479 + 6 = 9.31662479
x = 9.31662479

Simplifying
x = 9.31662479

Subproblem 2
x + -6 = -3.31662479

Simplifying
x + -6 = -3.31662479

Reorder the terms:
-6 + x = -3.31662479

Solving
-6 + x = -3.31662479

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -3.31662479 + 6

Combine like terms: -6 + 6 = 0
0 + x = -3.31662479 + 6
x = -3.31662479 + 6

Combine like terms: -3.31662479 + 6 = 2.68337521
x = 2.68337521

Simplifying
x = 2.68337521

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.31662479, 2.68337521}