0.2x(x-5)+1.2=0

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Solution for 0.2x(x-5)+1.2=0 equation: 


Simplifying
0.2x(x + -5) + 1.2 = 0

Reorder the terms:
0.2x(-5 + x) + 1.2 = 0
(-5 * 0.2x + x * 0.2x) + 1.2 = 0
(-1x + 0.2x2) + 1.2 = 0

Reorder the terms:
1.2 + -1x + 0.2x2 = 0

Solving
1.2 + -1x + 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 + -5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x + x2 = 0 + -6
-5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-5x + x2 = -6

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -6 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -6 + 6.25

Combine like terms: -6 + 6.25 = 0.25
6.25 + -5x + x2 = 0.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + -2.5) equal to 0.5 and -0.5.


Subproblem 1
x + -2.5 = 0.5

Simplifying
x + -2.5 = 0.5

Reorder the terms:
-2.5 + x = 0.5

Solving
-2.5 + x = 0.5

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 0.5 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 0.5 + 2.5
x = 0.5 + 2.5

Combine like terms: 0.5 + 2.5 = 3
x = 3

Simplifying
x = 3


Subproblem 2
x + -2.5 = -0.5

Simplifying
x + -2.5 = -0.5

Reorder the terms:
-2.5 + x = -0.5

Solving
-2.5 + x = -0.5

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -0.5 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -0.5 + 2.5
x = -0.5 + 2.5

Combine like terms: -0.5 + 2.5 = 2
x = 2

Simplifying
x = 2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3, 2}

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