x(x+2)=141

Solution for x(x+2)=141 equation:

Simplifying
x(x + 2) = 141

Reorder the terms:
x(2 + x) = 141
(2 * x + x * x) = 141
(2x + x2) = 141

Solving
2x + x2 = 141

Solving for variable 'x'.

Reorder the terms:
-141 + 2x + x2 = 141 + -141

Combine like terms: 141 + -141 = 0
-141 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '141' to each side of the equation.
-141 + 2x + 141 + x2 = 0 + 141

Reorder the terms:
-141 + 141 + 2x + x2 = 0 + 141

Combine like terms: -141 + 141 = 0
0 + 2x + x2 = 0 + 141
2x + x2 = 0 + 141

Combine like terms: 0 + 141 = 141
2x + x2 = 141

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 141 + 1

Reorder the terms:
1 + 2x + x2 = 141 + 1

Combine like terms: 141 + 1 = 142
1 + 2x + x2 = 142

Factor a perfect square on the left side:
(x + 1)(x + 1) = 142

Calculate the square root of the right side: 11.916375288

Break this problem into two subproblems by setting 
(x + 1) equal to 11.916375288 and -11.916375288.

Subproblem 1
x + 1 = 11.916375288

Simplifying
x + 1 = 11.916375288

Reorder the terms:
1 + x = 11.916375288

Solving
1 + x = 11.916375288

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 11.916375288 + -1

Combine like terms: 1 + -1 = 0
0 + x = 11.916375288 + -1
x = 11.916375288 + -1

Combine like terms: 11.916375288 + -1 = 10.916375288
x = 10.916375288

Simplifying
x = 10.916375288

Subproblem 2
x + 1 = -11.916375288

Simplifying
x + 1 = -11.916375288

Reorder the terms:
1 + x = -11.916375288

Solving
1 + x = -11.916375288

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -11.916375288 + -1

Combine like terms: 1 + -1 = 0
0 + x = -11.916375288 + -1
x = -11.916375288 + -1

Combine like terms: -11.916375288 + -1 = -12.916375288
x = -12.916375288

Simplifying
x = -12.916375288

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.916375288, -12.916375288}