(x+0.6)(x+4.4)=0

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Solution for (x+0.6)(x+4.4)=0 equation: 


Simplifying
(x + 0.6)(x + 4.4) = 0

Reorder the terms:
(0.6 + x)(x + 4.4) = 0

Reorder the terms:
(0.6 + x)(4.4 + x) = 0

Multiply (0.6 + x) * (4.4 + x)
(0.6(4.4 + x) + x(4.4 + x)) = 0
((4.4 * 0.6 + x * 0.6) + x(4.4 + x)) = 0
((2.64 + 0.6x) + x(4.4 + x)) = 0
(2.64 + 0.6x + (4.4 * x + x * x)) = 0
(2.64 + 0.6x + (4.4x + x2)) = 0

Combine like terms: 0.6x + 4.4x = 5x
(2.64 + 5x + x2) = 0

Solving
2.64 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.64' to each side of the equation.
2.64 + 5x + -2.64 + x2 = 0 + -2.64

Reorder the terms:
2.64 + -2.64 + 5x + x2 = 0 + -2.64

Combine like terms: 2.64 + -2.64 = 0.00
0.00 + 5x + x2 = 0 + -2.64
5x + x2 = 0 + -2.64

Combine like terms: 0 + -2.64 = -2.64
5x + x2 = -2.64

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -2.64 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -2.64 + 6.25

Combine like terms: -2.64 + 6.25 = 3.61
6.25 + 5x + x2 = 3.61

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 3.61

Calculate the square root of the right side: 1.9

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.9 and -1.9.


Subproblem 1
x + 2.5 = 1.9

Simplifying
x + 2.5 = 1.9

Reorder the terms:
2.5 + x = 1.9

Solving
2.5 + x = 1.9

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.9 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.9 + -2.5
x = 1.9 + -2.5

Combine like terms: 1.9 + -2.5 = -0.6
x = -0.6

Simplifying
x = -0.6


Subproblem 2
x + 2.5 = -1.9

Simplifying
x + 2.5 = -1.9

Reorder the terms:
2.5 + x = -1.9

Solving
2.5 + x = -1.9

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.9 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.9 + -2.5
x = -1.9 + -2.5

Combine like terms: -1.9 + -2.5 = -4.4
x = -4.4

Simplifying
x = -4.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.6, -4.4}

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