(x+1.1)(x-0.5)=0

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Solution for (x+1.1)(x-0.5)=0 equation: 


Simplifying
(x + 1.1)(x + -0.5) = 0

Reorder the terms:
(1.1 + x)(x + -0.5) = 0

Reorder the terms:
(1.1 + x)(-0.5 + x) = 0

Multiply (1.1 + x) * (-0.5 + x)
(1.1(-0.5 + x) + x(-0.5 + x)) = 0
((-0.5 * 1.1 + x * 1.1) + x(-0.5 + x)) = 0
((-0.55 + 1.1x) + x(-0.5 + x)) = 0
(-0.55 + 1.1x + (-0.5 * x + x * x)) = 0
(-0.55 + 1.1x + (-0.5x + x2)) = 0

Combine like terms: 1.1x + -0.5x = 0.6x
(-0.55 + 0.6x + x2) = 0

Solving
-0.55 + 0.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.55' to each side of the equation.
-0.55 + 0.6x + 0.55 + x2 = 0 + 0.55

Reorder the terms:
-0.55 + 0.55 + 0.6x + x2 = 0 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + 0.6x + x2 = 0 + 0.55
0.6x + x2 = 0 + 0.55

Combine like terms: 0 + 0.55 = 0.55
0.6x + x2 = 0.55

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 0.55 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.55 + 0.09

Combine like terms: 0.55 + 0.09 = 0.64
0.09 + 0.6x + x2 = 0.64

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.64

Calculate the square root of the right side: 0.8

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.8 and -0.8.


Subproblem 1
x + 0.3 = 0.8

Simplifying
x + 0.3 = 0.8

Reorder the terms:
0.3 + x = 0.8

Solving
0.3 + x = 0.8

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 0.8 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 0.8 + -0.3
x = 0.8 + -0.3

Combine like terms: 0.8 + -0.3 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 0.3 = -0.8

Simplifying
x + 0.3 = -0.8

Reorder the terms:
0.3 + x = -0.8

Solving
0.3 + x = -0.8

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -0.8 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -0.8 + -0.3
x = -0.8 + -0.3

Combine like terms: -0.8 + -0.3 = -1.1
x = -1.1

Simplifying
x = -1.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -1.1}

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