x(112-x)=127

Solution for x(112-x)=127 equation:

Simplifying
x(112 + -1x) = 127
(112 * x + -1x * x) = 127
(112x + -1x2) = 127

Solving
112x + -1x2 = 127

Solving for variable 'x'.

Reorder the terms:
-127 + 112x + -1x2 = 127 + -127

Combine like terms: 127 + -127 = 0
-127 + 112x + -1x2 = 0

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

Divide each side by '-1'.
127 + -112x + x2 = 0

Move the constant term to the right:

Add '-127' to each side of the equation.
127 + -112x + -127 + x2 = 0 + -127

Reorder the terms:
127 + -127 + -112x + x2 = 0 + -127

Combine like terms: 127 + -127 = 0
0 + -112x + x2 = 0 + -127
-112x + x2 = 0 + -127

Combine like terms: 0 + -127 = -127
-112x + x2 = -127

The x term is -112x.  Take half its coefficient (-56).
Square it (3136) and add it to both sides.

Add '3136' to each side of the equation.
-112x + 3136 + x2 = -127 + 3136

Reorder the terms:
3136 + -112x + x2 = -127 + 3136

Combine like terms: -127 + 3136 = 3009
3136 + -112x + x2 = 3009

Factor a perfect square on the left side:
(x + -56)(x + -56) = 3009

Calculate the square root of the right side: 54.854352608

Break this problem into two subproblems by setting 
(x + -56) equal to 54.854352608 and -54.854352608.

Subproblem 1
x + -56 = 54.854352608

Simplifying
x + -56 = 54.854352608

Reorder the terms:
-56 + x = 54.854352608

Solving
-56 + x = 54.854352608

Solving for variable 'x'.

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

Add '56' to each side of the equation.
-56 + 56 + x = 54.854352608 + 56

Combine like terms: -56 + 56 = 0
0 + x = 54.854352608 + 56
x = 54.854352608 + 56

Combine like terms: 54.854352608 + 56 = 110.854352608
x = 110.854352608

Simplifying
x = 110.854352608

Subproblem 2
x + -56 = -54.854352608

Simplifying
x + -56 = -54.854352608

Reorder the terms:
-56 + x = -54.854352608

Solving
-56 + x = -54.854352608

Solving for variable 'x'.

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

Add '56' to each side of the equation.
-56 + 56 + x = -54.854352608 + 56

Combine like terms: -56 + 56 = 0
0 + x = -54.854352608 + 56
x = -54.854352608 + 56

Combine like terms: -54.854352608 + 56 = 1.145647392
x = 1.145647392

Simplifying
x = 1.145647392

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {110.854352608, 1.145647392}