.2x^2+1.2x+1=0

Solution for .2x^2+1.2x+1=0 equation:

Simplifying
0.2x2 + 1.2x + 1 = 0

Reorder the terms:
1 + 1.2x + 0.2x2 = 0

Solving
1 + 1.2x + 0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.2 the coefficient of the squared term: 

Divide each side by '0.2'.
5 + 6x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 6x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 6x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x + x2 = 0 + -5
6x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
6x + x2 = -5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -5 + 9

Reorder the terms:
9 + 6x + x2 = -5 + 9

Combine like terms: -5 + 9 = 4
9 + 6x + x2 = 4

Factor a perfect square on the left side:
(x + 3)(x + 3) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 3) equal to 2 and -2.

Subproblem 1
x + 3 = 2

Simplifying
x + 3 = 2

Reorder the terms:
3 + x = 2

Solving
3 + x = 2

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2 + -3
x = 2 + -3

Combine like terms: 2 + -3 = -1
x = -1

Simplifying
x = -1

Subproblem 2
x + 3 = -2

Simplifying
x + 3 = -2

Reorder the terms:
3 + x = -2

Solving
3 + x = -2

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2 + -3
x = -2 + -3

Combine like terms: -2 + -3 = -5
x = -5

Simplifying
x = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1, -5}