Simplifying
x^{2} + 2x + 1 = 0
Reorder the terms:
1 + 2x + x^{2} = 0
Solving
1 + 2x + x^{2} = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '-1' to each side of the equation.
1 + 2x + -1 + x^{2} = 0 + -1
Reorder the terms:
1 + -1 + 2x + x^{2} = 0 + -1
Combine like terms: 1 + -1 = 0
0 + 2x + x^{2} = 0 + -1
2x + x^{2} = 0 + -1
Combine like terms: 0 + -1 = -1
2x + x^{2} = -1
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 + x^{2} = -1 + 1
Reorder the terms:
1 + 2x + x^{2} = -1 + 1
Combine like terms: -1 + 1 = 0
1 + 2x + x^{2} = 0
Factor a perfect square on the left side:
(x + 1)(x + 1) = 0
Calculate the square root of the right side: 0
Break this problem into two subproblems by setting
(x + 1) equal to 0 and 0.
#### Subproblem 1

x + 1 = 0
Simplifying
x + 1 = 0
Reorder the terms:
1 + x = 0
Solving
1 + x = 0
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 = 0 + -1
Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1
Combine like terms: 0 + -1 = -1
x = -1
Simplifying
x = -1
#### Subproblem 2

x + 1 = 0
Simplifying
x + 1 = 0
Reorder the terms:
1 + x = 0
Solving
1 + x = 0
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 = 0 + -1
Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1
Combine like terms: 0 + -1 = -1
x = -1
Simplifying
x = -1
#### Solution

The solution to the problem is based on the solutions
from the subproblems.
x = {-1, -1}