(x+.1)(x+4.1)=0

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Solution for (x+.1)(x+4.1)=0 equation: 


Simplifying
(x + 0.1)(x + 4.1) = 0

Reorder the terms:
(0.1 + x)(x + 4.1) = 0

Reorder the terms:
(0.1 + x)(4.1 + x) = 0

Multiply (0.1 + x) * (4.1 + x)
(0.1(4.1 + x) + x(4.1 + x)) = 0
((4.1 * 0.1 + x * 0.1) + x(4.1 + x)) = 0
((0.41 + 0.1x) + x(4.1 + x)) = 0
(0.41 + 0.1x + (4.1 * x + x * x)) = 0
(0.41 + 0.1x + (4.1x + x2)) = 0

Combine like terms: 0.1x + 4.1x = 4.2x
(0.41 + 4.2x + x2) = 0

Solving
0.41 + 4.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.41' to each side of the equation.
0.41 + 4.2x + -0.41 + x2 = 0 + -0.41

Reorder the terms:
0.41 + -0.41 + 4.2x + x2 = 0 + -0.41

Combine like terms: 0.41 + -0.41 = 0.00
0.00 + 4.2x + x2 = 0 + -0.41
4.2x + x2 = 0 + -0.41

Combine like terms: 0 + -0.41 = -0.41
4.2x + x2 = -0.41

The x term is 4.2x.  Take half its coefficient (2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
4.2x + 4.41 + x2 = -0.41 + 4.41

Reorder the terms:
4.41 + 4.2x + x2 = -0.41 + 4.41

Combine like terms: -0.41 + 4.41 = 4
4.41 + 4.2x + x2 = 4

Factor a perfect square on the left side:
(x + 2.1)(x + 2.1) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 2.1) equal to 2 and -2.


Subproblem 1
x + 2.1 = 2

Simplifying
x + 2.1 = 2

Reorder the terms:
2.1 + x = 2

Solving
2.1 + x = 2

Solving for variable 'x'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + x = 2 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = 2 + -2.1
x = 2 + -2.1

Combine like terms: 2 + -2.1 = -0.1
x = -0.1

Simplifying
x = -0.1


Subproblem 2
x + 2.1 = -2

Simplifying
x + 2.1 = -2

Reorder the terms:
2.1 + x = -2

Solving
2.1 + x = -2

Solving for variable 'x'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + x = -2 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = -2 + -2.1
x = -2 + -2.1

Combine like terms: -2 + -2.1 = -4.1
x = -4.1

Simplifying
x = -4.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1, -4.1}

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