-0.2(x-1.9)(x-3.5)=0

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Solution for -0.2(x-1.9)(x-3.5)=0 equation: 


Simplifying
-0.2(x + -1.9)(x + -3.5) = 0

Reorder the terms:
-0.2(-1.9 + x)(x + -3.5) = 0

Reorder the terms:
-0.2(-1.9 + x)(-3.5 + x) = 0

Multiply (-1.9 + x) * (-3.5 + x)
-0.2(-1.9(-3.5 + x) + x(-3.5 + x)) = 0
-0.2((-3.5 * -1.9 + x * -1.9) + x(-3.5 + x)) = 0
-0.2((6.65 + -1.9x) + x(-3.5 + x)) = 0
-0.2(6.65 + -1.9x + (-3.5 * x + x * x)) = 0
-0.2(6.65 + -1.9x + (-3.5x + x2)) = 0

Combine like terms: -1.9x + -3.5x = -5.4x
-0.2(6.65 + -5.4x + x2) = 0
(6.65 * -0.2 + -5.4x * -0.2 + x2 * -0.2) = 0
(-1.33 + 1.08x + -0.2x2) = 0

Solving
-1.33 + 1.08x + -0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
6.65 + -5.4x + x2 = 0

Move the constant term to the right:

Add '-6.65' to each side of the equation.
6.65 + -5.4x + -6.65 + x2 = 0 + -6.65

Reorder the terms:
6.65 + -6.65 + -5.4x + x2 = 0 + -6.65

Combine like terms: 6.65 + -6.65 = 0.00
0.00 + -5.4x + x2 = 0 + -6.65
-5.4x + x2 = 0 + -6.65

Combine like terms: 0 + -6.65 = -6.65
-5.4x + x2 = -6.65

The x term is -5.4x.  Take half its coefficient (-2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
-5.4x + 7.29 + x2 = -6.65 + 7.29

Reorder the terms:
7.29 + -5.4x + x2 = -6.65 + 7.29

Combine like terms: -6.65 + 7.29 = 0.64
7.29 + -5.4x + x2 = 0.64

Factor a perfect square on the left side:
(x + -2.7)(x + -2.7) = 0.64

Calculate the square root of the right side: 0.8

Break this problem into two subproblems by setting 
(x + -2.7) equal to 0.8 and -0.8.


Subproblem 1
x + -2.7 = 0.8

Simplifying
x + -2.7 = 0.8

Reorder the terms:
-2.7 + x = 0.8

Solving
-2.7 + x = 0.8

Solving for variable 'x'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + x = 0.8 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + x = 0.8 + 2.7
x = 0.8 + 2.7

Combine like terms: 0.8 + 2.7 = 3.5
x = 3.5

Simplifying
x = 3.5


Subproblem 2
x + -2.7 = -0.8

Simplifying
x + -2.7 = -0.8

Reorder the terms:
-2.7 + x = -0.8

Solving
-2.7 + x = -0.8

Solving for variable 'x'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + x = -0.8 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + x = -0.8 + 2.7
x = -0.8 + 2.7

Combine like terms: -0.8 + 2.7 = 1.9
x = 1.9

Simplifying
x = 1.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, 1.9}

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