0.2x(x-8)=4

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Solution for 0.2x(x-8)=4 equation: 


Simplifying
0.2x(x + -8) = 4

Reorder the terms:
0.2x(-8 + x) = 4
(-8 * 0.2x + x * 0.2x) = 4
(-1.6x + 0.2x2) = 4

Solving
-1.6x + 0.2x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -1.6x + 0.2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -1.6x + 0.2x2 = 0

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

Divide each side by '0.2'.
-20 + -8x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -8x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -8x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -8x + x2 = 0 + 20
-8x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-8x + x2 = 20

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 20 + 16

Reorder the terms:
16 + -8x + x2 = 20 + 16

Combine like terms: 20 + 16 = 36
16 + -8x + x2 = 36

Factor a perfect square on the left side:
(x + -4)(x + -4) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + -4) equal to 6 and -6.


Subproblem 1
x + -4 = 6

Simplifying
x + -4 = 6

Reorder the terms:
-4 + x = 6

Solving
-4 + x = 6

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 6 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6 + 4
x = 6 + 4

Combine like terms: 6 + 4 = 10
x = 10

Simplifying
x = 10


Subproblem 2
x + -4 = -6

Simplifying
x + -4 = -6

Reorder the terms:
-4 + x = -6

Solving
-4 + x = -6

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -6 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6 + 4
x = -6 + 4

Combine like terms: -6 + 4 = -2
x = -2

Simplifying
x = -2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10, -2}

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