5x(10-x)=55-25x-5x

Solution for 5x(10-x)=55-25x-5x equation:

Simplifying
5x(10 + -1x) = 55 + -25x + -5x
(10 * 5x + -1x * 5x) = 55 + -25x + -5x
(50x + -5x2) = 55 + -25x + -5x

Combine like terms: -25x + -5x = -30x
50x + -5x2 = 55 + -30x

Solving
50x + -5x2 = 55 + -30x

Solving for variable 'x'.

Reorder the terms:
-55 + 50x + 30x + -5x2 = 55 + -30x + -55 + 30x

Combine like terms: 50x + 30x = 80x
-55 + 80x + -5x2 = 55 + -30x + -55 + 30x

Reorder the terms:
-55 + 80x + -5x2 = 55 + -55 + -30x + 30x

Combine like terms: 55 + -55 = 0
-55 + 80x + -5x2 = 0 + -30x + 30x
-55 + 80x + -5x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
-55 + 80x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-11 + 16x + -1x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-11 + 16x + -1x2)' equal to zero and attempt to solve:

Simplifying
-11 + 16x + -1x2 = 0

Solving
-11 + 16x + -1x2 = 0

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

Divide each side by '-1'.
11 + -16x + x2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -16x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -16x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -16x + x2 = 0 + -11
-16x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-16x + x2 = -11

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -11 + 64

Reorder the terms:
64 + -16x + x2 = -11 + 64

Combine like terms: -11 + 64 = 53
64 + -16x + x2 = 53

Factor a perfect square on the left side:
(x + -8)(x + -8) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(x + -8) equal to 7.280109889 and -7.280109889.

Subproblem 1
x + -8 = 7.280109889

Simplifying
x + -8 = 7.280109889

Reorder the terms:
-8 + x = 7.280109889

Solving
-8 + x = 7.280109889

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 7.280109889 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.280109889 + 8
x = 7.280109889 + 8

Combine like terms: 7.280109889 + 8 = 15.280109889
x = 15.280109889

Simplifying
x = 15.280109889

Subproblem 2
x + -8 = -7.280109889

Simplifying
x + -8 = -7.280109889

Reorder the terms:
-8 + x = -7.280109889

Solving
-8 + x = -7.280109889

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -7.280109889 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.280109889 + 8
x = -7.280109889 + 8

Combine like terms: -7.280109889 + 8 = 0.719890111
x = 0.719890111

Simplifying
x = 0.719890111

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.280109889, 0.719890111}
Solution
x = {15.280109889, 0.719890111}