x(x-1)=139

Solution for x(x-1)=139 equation:

Simplifying
x(x + -1) = 139

Reorder the terms:
x(-1 + x) = 139
(-1 * x + x * x) = 139
(-1x + x2) = 139

Solving
-1x + x2 = 139

Solving for variable 'x'.

Reorder the terms:
-139 + -1x + x2 = 139 + -139

Combine like terms: 139 + -139 = 0
-139 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '139' to each side of the equation.
-139 + -1x + 139 + x2 = 0 + 139

Reorder the terms:
-139 + 139 + -1x + x2 = 0 + 139

Combine like terms: -139 + 139 = 0
0 + -1x + x2 = 0 + 139
-1x + x2 = 0 + 139

Combine like terms: 0 + 139 = 139
-1x + x2 = 139

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 139 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 139 + 0.25

Combine like terms: 139 + 0.25 = 139.25
0.25 + -1x + x2 = 139.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 139.25

Calculate the square root of the right side: 11.800423721

Break this problem into two subproblems by setting 
(x + -0.5) equal to 11.800423721 and -11.800423721.

Subproblem 1
x + -0.5 = 11.800423721

Simplifying
x + -0.5 = 11.800423721

Reorder the terms:
-0.5 + x = 11.800423721

Solving
-0.5 + x = 11.800423721

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 11.800423721 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 11.800423721 + 0.5
x = 11.800423721 + 0.5

Combine like terms: 11.800423721 + 0.5 = 12.300423721
x = 12.300423721

Simplifying
x = 12.300423721

Subproblem 2
x + -0.5 = -11.800423721

Simplifying
x + -0.5 = -11.800423721

Reorder the terms:
-0.5 + x = -11.800423721

Solving
-0.5 + x = -11.800423721

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -11.800423721 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -11.800423721 + 0.5
x = -11.800423721 + 0.5

Combine like terms: -11.800423721 + 0.5 = -11.300423721
x = -11.300423721

Simplifying
x = -11.300423721

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.300423721, -11.300423721}