x^2+2.1*x+0.2=0

Solution for x^2+2.1*x+0.2=0 equation:

Simplifying
x2 + 2.1x + 0.2 = 0

Reorder the terms:
0.2 + 2.1x + x2 = 0

Solving
0.2 + 2.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2.1x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2.1x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2.1x + x2 = 0 + -0.2
2.1x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2.1x + x2 = -0.2

The x term is 2.1x.  Take half its coefficient (1.05).
Square it (1.1025) and add it to both sides.

Add '1.1025' to each side of the equation.
2.1x + 1.1025 + x2 = -0.2 + 1.1025

Reorder the terms:
1.1025 + 2.1x + x2 = -0.2 + 1.1025

Combine like terms: -0.2 + 1.1025 = 0.9025
1.1025 + 2.1x + x2 = 0.9025

Factor a perfect square on the left side:
(x + 1.05)(x + 1.05) = 0.9025

Calculate the square root of the right side: 0.95

Break this problem into two subproblems by setting 
(x + 1.05) equal to 0.95 and -0.95.

Subproblem 1
x + 1.05 = 0.95

Simplifying
x + 1.05 = 0.95

Reorder the terms:
1.05 + x = 0.95

Solving
1.05 + x = 0.95

Solving for variable 'x'.

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

Add '-1.05' to each side of the equation.
1.05 + -1.05 + x = 0.95 + -1.05

Combine like terms: 1.05 + -1.05 = 0.00
0.00 + x = 0.95 + -1.05
x = 0.95 + -1.05

Combine like terms: 0.95 + -1.05 = -0.1
x = -0.1

Simplifying
x = -0.1

Subproblem 2
x + 1.05 = -0.95

Simplifying
x + 1.05 = -0.95

Reorder the terms:
1.05 + x = -0.95

Solving
1.05 + x = -0.95

Solving for variable 'x'.

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

Add '-1.05' to each side of the equation.
1.05 + -1.05 + x = -0.95 + -1.05

Combine like terms: 1.05 + -1.05 = 0.00
0.00 + x = -0.95 + -1.05
x = -0.95 + -1.05

Combine like terms: -0.95 + -1.05 = -2
x = -2

Simplifying
x = -2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1, -2}