x(x+1)=121

Solution for x(x+1)=121 equation:

Simplifying
x(x + 1) = 121

Reorder the terms:
x(1 + x) = 121
(1 * x + x * x) = 121
(1x + x2) = 121

Solving
1x + x2 = 121

Solving for variable 'x'.

Reorder the terms:
-121 + 1x + x2 = 121 + -121

Combine like terms: 121 + -121 = 0
-121 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + 1x + 121 + x2 = 0 + 121

Reorder the terms:
-121 + 121 + 1x + x2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + 1x + x2 = 0 + 121
1x + x2 = 0 + 121

Combine like terms: 0 + 121 = 121
1x + x2 = 121

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.
x + 0.25 + x2 = 121 + 0.25

Reorder the terms:
0.25 + x + x2 = 121 + 0.25

Combine like terms: 121 + 0.25 = 121.25
0.25 + x + x2 = 121.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 121.25

Calculate the square root of the right side: 11.011357773

Break this problem into two subproblems by setting 
(x + 0.5) equal to 11.011357773 and -11.011357773.

Subproblem 1
x + 0.5 = 11.011357773

Simplifying
x + 0.5 = 11.011357773

Reorder the terms:
0.5 + x = 11.011357773

Solving
0.5 + x = 11.011357773

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 = 11.011357773 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 11.011357773 + -0.5
x = 11.011357773 + -0.5

Combine like terms: 11.011357773 + -0.5 = 10.511357773
x = 10.511357773

Simplifying
x = 10.511357773

Subproblem 2
x + 0.5 = -11.011357773

Simplifying
x + 0.5 = -11.011357773

Reorder the terms:
0.5 + x = -11.011357773

Solving
0.5 + x = -11.011357773

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 = -11.011357773 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -11.011357773 + -0.5
x = -11.011357773 + -0.5

Combine like terms: -11.011357773 + -0.5 = -11.511357773
x = -11.511357773

Simplifying
x = -11.511357773

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.511357773, -11.511357773}