(x+0.3)(x+2.2)=0

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Solution for (x+0.3)(x+2.2)=0 equation: 


Simplifying
(x + 0.3)(x + 2.2) = 0

Reorder the terms:
(0.3 + x)(x + 2.2) = 0

Reorder the terms:
(0.3 + x)(2.2 + x) = 0

Multiply (0.3 + x) * (2.2 + x)
(0.3(2.2 + x) + x(2.2 + x)) = 0
((2.2 * 0.3 + x * 0.3) + x(2.2 + x)) = 0
((0.66 + 0.3x) + x(2.2 + x)) = 0
(0.66 + 0.3x + (2.2 * x + x * x)) = 0
(0.66 + 0.3x + (2.2x + x2)) = 0

Combine like terms: 0.3x + 2.2x = 2.5x
(0.66 + 2.5x + x2) = 0

Solving
0.66 + 2.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.66' to each side of the equation.
0.66 + 2.5x + -0.66 + x2 = 0 + -0.66

Reorder the terms:
0.66 + -0.66 + 2.5x + x2 = 0 + -0.66

Combine like terms: 0.66 + -0.66 = 0.00
0.00 + 2.5x + x2 = 0 + -0.66
2.5x + x2 = 0 + -0.66

Combine like terms: 0 + -0.66 = -0.66
2.5x + x2 = -0.66

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -0.66 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -0.66 + 1.5625

Combine like terms: -0.66 + 1.5625 = 0.9025
1.5625 + 2.5x + x2 = 0.9025

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 0.9025

Calculate the square root of the right side: 0.95

Break this problem into two subproblems by setting 
(x + 1.25) equal to 0.95 and -0.95.


Subproblem 1
x + 1.25 = 0.95

Simplifying
x + 1.25 = 0.95

Reorder the terms:
1.25 + x = 0.95

Solving
1.25 + x = 0.95

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 0.95 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 0.95 + -1.25
x = 0.95 + -1.25

Combine like terms: 0.95 + -1.25 = -0.3
x = -0.3

Simplifying
x = -0.3


Subproblem 2
x + 1.25 = -0.95

Simplifying
x + 1.25 = -0.95

Reorder the terms:
1.25 + x = -0.95

Solving
1.25 + x = -0.95

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -0.95 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -0.95 + -1.25
x = -0.95 + -1.25

Combine like terms: -0.95 + -1.25 = -2.2
x = -2.2

Simplifying
x = -2.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.3, -2.2}

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