(x+0.1)(x+4.5)=0

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Solution for (x+0.1)(x+4.5)=0 equation: 


Simplifying
(x + 0.1)(x + 4.5) = 0

Reorder the terms:
(0.1 + x)(x + 4.5) = 0

Reorder the terms:
(0.1 + x)(4.5 + x) = 0

Multiply (0.1 + x) * (4.5 + x)
(0.1(4.5 + x) + x(4.5 + x)) = 0
((4.5 * 0.1 + x * 0.1) + x(4.5 + x)) = 0
((0.45 + 0.1x) + x(4.5 + x)) = 0
(0.45 + 0.1x + (4.5 * x + x * x)) = 0
(0.45 + 0.1x + (4.5x + x2)) = 0

Combine like terms: 0.1x + 4.5x = 4.6x
(0.45 + 4.6x + x2) = 0

Solving
0.45 + 4.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.45' to each side of the equation.
0.45 + 4.6x + -0.45 + x2 = 0 + -0.45

Reorder the terms:
0.45 + -0.45 + 4.6x + x2 = 0 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + 4.6x + x2 = 0 + -0.45
4.6x + x2 = 0 + -0.45

Combine like terms: 0 + -0.45 = -0.45
4.6x + x2 = -0.45

The x term is 4.6x.  Take half its coefficient (2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
4.6x + 5.29 + x2 = -0.45 + 5.29

Reorder the terms:
5.29 + 4.6x + x2 = -0.45 + 5.29

Combine like terms: -0.45 + 5.29 = 4.84
5.29 + 4.6x + x2 = 4.84

Factor a perfect square on the left side:
(x + 2.3)(x + 2.3) = 4.84

Calculate the square root of the right side: 2.2

Break this problem into two subproblems by setting 
(x + 2.3) equal to 2.2 and -2.2.


Subproblem 1
x + 2.3 = 2.2

Simplifying
x + 2.3 = 2.2

Reorder the terms:
2.3 + x = 2.2

Solving
2.3 + x = 2.2

Solving for variable 'x'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + x = 2.2 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + x = 2.2 + -2.3
x = 2.2 + -2.3

Combine like terms: 2.2 + -2.3 = -0.1
x = -0.1

Simplifying
x = -0.1


Subproblem 2
x + 2.3 = -2.2

Simplifying
x + 2.3 = -2.2

Reorder the terms:
2.3 + x = -2.2

Solving
2.3 + x = -2.2

Solving for variable 'x'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + x = -2.2 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + x = -2.2 + -2.3
x = -2.2 + -2.3

Combine like terms: -2.2 + -2.3 = -4.5
x = -4.5

Simplifying
x = -4.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1, -4.5}

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