x^2+2.21x+1.21=0

Solution for x^2+2.21x+1.21=0 equation:

Simplifying
x2 + 2.21x + 1.21 = 0

Reorder the terms:
1.21 + 2.21x + x2 = 0

Solving
1.21 + 2.21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.21' to each side of the equation.
1.21 + 2.21x + -1.21 + x2 = 0 + -1.21

Reorder the terms:
1.21 + -1.21 + 2.21x + x2 = 0 + -1.21

Combine like terms: 1.21 + -1.21 = 0.00
0.00 + 2.21x + x2 = 0 + -1.21
2.21x + x2 = 0 + -1.21

Combine like terms: 0 + -1.21 = -1.21
2.21x + x2 = -1.21

The x term is 2.21x.  Take half its coefficient (1.105).
Square it (1.221025) and add it to both sides.

Add '1.221025' to each side of the equation.
2.21x + 1.221025 + x2 = -1.21 + 1.221025

Reorder the terms:
1.221025 + 2.21x + x2 = -1.21 + 1.221025

Combine like terms: -1.21 + 1.221025 = 0.011025
1.221025 + 2.21x + x2 = 0.011025

Factor a perfect square on the left side:
(x + 1.105)(x + 1.105) = 0.011025

Calculate the square root of the right side: 0.105

Break this problem into two subproblems by setting 
(x + 1.105) equal to 0.105 and -0.105.

Subproblem 1
x + 1.105 = 0.105

Simplifying
x + 1.105 = 0.105

Reorder the terms:
1.105 + x = 0.105

Solving
1.105 + x = 0.105

Solving for variable 'x'.

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

Add '-1.105' to each side of the equation.
1.105 + -1.105 + x = 0.105 + -1.105

Combine like terms: 1.105 + -1.105 = 0.000
0.000 + x = 0.105 + -1.105
x = 0.105 + -1.105

Combine like terms: 0.105 + -1.105 = -1
x = -1

Simplifying
x = -1

Subproblem 2
x + 1.105 = -0.105

Simplifying
x + 1.105 = -0.105

Reorder the terms:
1.105 + x = -0.105

Solving
1.105 + x = -0.105

Solving for variable 'x'.

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

Add '-1.105' to each side of the equation.
1.105 + -1.105 + x = -0.105 + -1.105

Combine like terms: 1.105 + -1.105 = 0.000
0.000 + x = -0.105 + -1.105
x = -0.105 + -1.105

Combine like terms: -0.105 + -1.105 = -1.21
x = -1.21

Simplifying
x = -1.21

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1, -1.21}