(x+0.1)(x+4.7)=0

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Solution for (x+0.1)(x+4.7)=0 equation: 


Simplifying
(x + 0.1)(x + 4.7) = 0

Reorder the terms:
(0.1 + x)(x + 4.7) = 0

Reorder the terms:
(0.1 + x)(4.7 + x) = 0

Multiply (0.1 + x) * (4.7 + x)
(0.1(4.7 + x) + x(4.7 + x)) = 0
((4.7 * 0.1 + x * 0.1) + x(4.7 + x)) = 0
((0.47 + 0.1x) + x(4.7 + x)) = 0
(0.47 + 0.1x + (4.7 * x + x * x)) = 0
(0.47 + 0.1x + (4.7x + x2)) = 0

Combine like terms: 0.1x + 4.7x = 4.8x
(0.47 + 4.8x + x2) = 0

Solving
0.47 + 4.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.47' to each side of the equation.
0.47 + 4.8x + -0.47 + x2 = 0 + -0.47

Reorder the terms:
0.47 + -0.47 + 4.8x + x2 = 0 + -0.47

Combine like terms: 0.47 + -0.47 = 0.00
0.00 + 4.8x + x2 = 0 + -0.47
4.8x + x2 = 0 + -0.47

Combine like terms: 0 + -0.47 = -0.47
4.8x + x2 = -0.47

The x term is 4.8x.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8x + 5.76 + x2 = -0.47 + 5.76

Reorder the terms:
5.76 + 4.8x + x2 = -0.47 + 5.76

Combine like terms: -0.47 + 5.76 = 5.29
5.76 + 4.8x + x2 = 5.29

Factor a perfect square on the left side:
(x + 2.4)(x + 2.4) = 5.29

Calculate the square root of the right side: 2.3

Break this problem into two subproblems by setting 
(x + 2.4) equal to 2.3 and -2.3.


Subproblem 1
x + 2.4 = 2.3

Simplifying
x + 2.4 = 2.3

Reorder the terms:
2.4 + x = 2.3

Solving
2.4 + x = 2.3

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = 2.3 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = 2.3 + -2.4
x = 2.3 + -2.4

Combine like terms: 2.3 + -2.4 = -0.1
x = -0.1

Simplifying
x = -0.1


Subproblem 2
x + 2.4 = -2.3

Simplifying
x + 2.4 = -2.3

Reorder the terms:
2.4 + x = -2.3

Solving
2.4 + x = -2.3

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = -2.3 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = -2.3 + -2.4
x = -2.3 + -2.4

Combine like terms: -2.3 + -2.4 = -4.7
x = -4.7

Simplifying
x = -4.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1, -4.7}

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