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Simplifying
x2 + 2x + 1 = 0

Reorder the terms:
1 + 2x + x2 = 0

Solving
1 + 2x + x2 = 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 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 2x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x + x2 = 0 + -1
2x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
2x + x2 = -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 + x2 = -1 + 1

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

Combine like terms: -1 + 1 = 0
1 + 2x + x2 = 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}
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