(x-0.5)*(0.2+x)=0

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Solution for (x-0.5)*(0.2+x)=0 equation: 


Simplifying
(x + -0.5)(0.2 + x) = 0

Reorder the terms:
(-0.5 + x)(0.2 + x) = 0

Multiply (-0.5 + x) * (0.2 + x)
(-0.5(0.2 + x) + x(0.2 + x)) = 0
((0.2 * -0.5 + x * -0.5) + x(0.2 + x)) = 0
((-0.1 + -0.5x) + x(0.2 + x)) = 0
(-0.1 + -0.5x + (0.2 * x + x * x)) = 0
(-0.1 + -0.5x + (0.2x + x2)) = 0

Combine like terms: -0.5x + 0.2x = -0.3x
(-0.1 + -0.3x + x2) = 0

Solving
-0.1 + -0.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -0.3x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -0.3x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -0.3x + x2 = 0 + 0.1
-0.3x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-0.3x + x2 = 0.1

The x term is -0.3x.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3x + 0.0225 + x2 = 0.1 + 0.0225

Reorder the terms:
0.0225 + -0.3x + x2 = 0.1 + 0.0225

Combine like terms: 0.1 + 0.0225 = 0.1225
0.0225 + -0.3x + x2 = 0.1225

Factor a perfect square on the left side:
(x + -0.15)(x + -0.15) = 0.1225

Calculate the square root of the right side: 0.35

Break this problem into two subproblems by setting 
(x + -0.15) equal to 0.35 and -0.35.


Subproblem 1
x + -0.15 = 0.35

Simplifying
x + -0.15 = 0.35

Reorder the terms:
-0.15 + x = 0.35

Solving
-0.15 + x = 0.35

Solving for variable 'x'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + x = 0.35 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + x = 0.35 + 0.15
x = 0.35 + 0.15

Combine like terms: 0.35 + 0.15 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + -0.15 = -0.35

Simplifying
x + -0.15 = -0.35

Reorder the terms:
-0.15 + x = -0.35

Solving
-0.15 + x = -0.35

Solving for variable 'x'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + x = -0.35 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + x = -0.35 + 0.15
x = -0.35 + 0.15

Combine like terms: -0.35 + 0.15 = -0.2
x = -0.2

Simplifying
x = -0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -0.2}

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