x^2+2.6x+1.65=0

Solution for x^2+2.6x+1.65=0 equation:

Simplifying
x2 + 2.6x + 1.65 = 0

Reorder the terms:
1.65 + 2.6x + x2 = 0

Solving
1.65 + 2.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.65' to each side of the equation.
1.65 + 2.6x + -1.65 + x2 = 0 + -1.65

Reorder the terms:
1.65 + -1.65 + 2.6x + x2 = 0 + -1.65

Combine like terms: 1.65 + -1.65 = 0.00
0.00 + 2.6x + x2 = 0 + -1.65
2.6x + x2 = 0 + -1.65

Combine like terms: 0 + -1.65 = -1.65
2.6x + x2 = -1.65

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = -1.65 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = -1.65 + 1.69

Combine like terms: -1.65 + 1.69 = 0.04
1.69 + 2.6x + x2 = 0.04

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 0.04

Calculate the square root of the right side: 0.2

Break this problem into two subproblems by setting 
(x + 1.3) equal to 0.2 and -0.2.

Subproblem 1
x + 1.3 = 0.2

Simplifying
x + 1.3 = 0.2

Reorder the terms:
1.3 + x = 0.2

Solving
1.3 + x = 0.2

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = 0.2 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = 0.2 + -1.3
x = 0.2 + -1.3

Combine like terms: 0.2 + -1.3 = -1.1
x = -1.1

Simplifying
x = -1.1

Subproblem 2
x + 1.3 = -0.2

Simplifying
x + 1.3 = -0.2

Reorder the terms:
1.3 + x = -0.2

Solving
1.3 + x = -0.2

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = -0.2 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = -0.2 + -1.3
x = -0.2 + -1.3

Combine like terms: -0.2 + -1.3 = -1.5
x = -1.5

Simplifying
x = -1.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.1, -1.5}