(x+0.2)(x+3.2)=

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Solution for (x+0.2)(x+3.2)= equation: 


Simplifying
(x + 0.2)(x + 3.2) = 0

Reorder the terms:
(0.2 + x)(x + 3.2) = 0

Reorder the terms:
(0.2 + x)(3.2 + x) = 0

Multiply (0.2 + x) * (3.2 + x)
(0.2(3.2 + x) + x(3.2 + x)) = 0
((3.2 * 0.2 + x * 0.2) + x(3.2 + x)) = 0
((0.64 + 0.2x) + x(3.2 + x)) = 0
(0.64 + 0.2x + (3.2 * x + x * x)) = 0
(0.64 + 0.2x + (3.2x + x2)) = 0

Combine like terms: 0.2x + 3.2x = 3.4x
(0.64 + 3.4x + x2) = 0

Solving
0.64 + 3.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.64' to each side of the equation.
0.64 + 3.4x + -0.64 + x2 = 0 + -0.64

Reorder the terms:
0.64 + -0.64 + 3.4x + x2 = 0 + -0.64

Combine like terms: 0.64 + -0.64 = 0.00
0.00 + 3.4x + x2 = 0 + -0.64
3.4x + x2 = 0 + -0.64

Combine like terms: 0 + -0.64 = -0.64
3.4x + x2 = -0.64

The x term is 3.4x.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4x + 2.89 + x2 = -0.64 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = -0.64 + 2.89

Combine like terms: -0.64 + 2.89 = 2.25
2.89 + 3.4x + x2 = 2.25

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x + 1.7) equal to 1.5 and -1.5.


Subproblem 1
x + 1.7 = 1.5

Simplifying
x + 1.7 = 1.5

Reorder the terms:
1.7 + x = 1.5

Solving
1.7 + x = 1.5

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = 1.5 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 1.5 + -1.7
x = 1.5 + -1.7

Combine like terms: 1.5 + -1.7 = -0.2
x = -0.2

Simplifying
x = -0.2


Subproblem 2
x + 1.7 = -1.5

Simplifying
x + 1.7 = -1.5

Reorder the terms:
1.7 + x = -1.5

Solving
1.7 + x = -1.5

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = -1.5 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -1.5 + -1.7
x = -1.5 + -1.7

Combine like terms: -1.5 + -1.7 = -3.2
x = -3.2

Simplifying
x = -3.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.2, -3.2}

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