(x+0.6)(x+1.6)=0

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Solution for (x+0.6)(x+1.6)=0 equation: 


Simplifying
(x + 0.6)(x + 1.6) = 0

Reorder the terms:
(0.6 + x)(x + 1.6) = 0

Reorder the terms:
(0.6 + x)(1.6 + x) = 0

Multiply (0.6 + x) * (1.6 + x)
(0.6(1.6 + x) + x(1.6 + x)) = 0
((1.6 * 0.6 + x * 0.6) + x(1.6 + x)) = 0
((0.96 + 0.6x) + x(1.6 + x)) = 0
(0.96 + 0.6x + (1.6 * x + x * x)) = 0
(0.96 + 0.6x + (1.6x + x2)) = 0

Combine like terms: 0.6x + 1.6x = 2.2x
(0.96 + 2.2x + x2) = 0

Solving
0.96 + 2.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.96' to each side of the equation.
0.96 + 2.2x + -0.96 + x2 = 0 + -0.96

Reorder the terms:
0.96 + -0.96 + 2.2x + x2 = 0 + -0.96

Combine like terms: 0.96 + -0.96 = 0.00
0.00 + 2.2x + x2 = 0 + -0.96
2.2x + x2 = 0 + -0.96

Combine like terms: 0 + -0.96 = -0.96
2.2x + x2 = -0.96

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = -0.96 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = -0.96 + 1.21

Combine like terms: -0.96 + 1.21 = 0.25
1.21 + 2.2x + x2 = 0.25

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + 1.1) equal to 0.5 and -0.5.


Subproblem 1
x + 1.1 = 0.5

Simplifying
x + 1.1 = 0.5

Reorder the terms:
1.1 + x = 0.5

Solving
1.1 + x = 0.5

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = 0.5 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = 0.5 + -1.1
x = 0.5 + -1.1

Combine like terms: 0.5 + -1.1 = -0.6
x = -0.6

Simplifying
x = -0.6


Subproblem 2
x + 1.1 = -0.5

Simplifying
x + 1.1 = -0.5

Reorder the terms:
1.1 + x = -0.5

Solving
1.1 + x = -0.5

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = -0.5 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = -0.5 + -1.1
x = -0.5 + -1.1

Combine like terms: -0.5 + -1.1 = -1.6
x = -1.6

Simplifying
x = -1.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.6, -1.6}

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