-0.8x(x-9)=1.2x+5.2

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Solution for -0.8x(x-9)=1.2x+5.2 equation: 


Simplifying
-0.8x(x + -9) = 1.2x + 5.2

Reorder the terms:
-0.8x(-9 + x) = 1.2x + 5.2
(-9 * -0.8x + x * -0.8x) = 1.2x + 5.2
(7.2x + -0.8x2) = 1.2x + 5.2

Reorder the terms:
7.2x + -0.8x2 = 5.2 + 1.2x

Solving
7.2x + -0.8x2 = 5.2 + 1.2x

Solving for variable 'x'.

Reorder the terms:
-5.2 + 7.2x + -1.2x + -0.8x2 = 5.2 + 1.2x + -5.2 + -1.2x

Combine like terms: 7.2x + -1.2x = 6x
-5.2 + 6x + -0.8x2 = 5.2 + 1.2x + -5.2 + -1.2x

Reorder the terms:
-5.2 + 6x + -0.8x2 = 5.2 + -5.2 + 1.2x + -1.2x

Combine like terms: 5.2 + -5.2 = 0.0
-5.2 + 6x + -0.8x2 = 0.0 + 1.2x + -1.2x
-5.2 + 6x + -0.8x2 = 1.2x + -1.2x

Combine like terms: 1.2x + -1.2x = 0.0
-5.2 + 6x + -0.8x2 = 0.0

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
6.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -7.5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -7.5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -7.5x + x2 = 0 + -6.5
-7.5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-7.5x + x2 = -6.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -6.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -6.5 + 14.0625

Combine like terms: -6.5 + 14.0625 = 7.5625
14.0625 + -7.5x + x2 = 7.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(x + -3.75) equal to 2.75 and -2.75.


Subproblem 1
x + -3.75 = 2.75

Simplifying
x + -3.75 = 2.75

Reorder the terms:
-3.75 + x = 2.75

Solving
-3.75 + x = 2.75

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 2.75 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 2.75 + 3.75
x = 2.75 + 3.75

Combine like terms: 2.75 + 3.75 = 6.5
x = 6.5

Simplifying
x = 6.5


Subproblem 2
x + -3.75 = -2.75

Simplifying
x + -3.75 = -2.75

Reorder the terms:
-3.75 + x = -2.75

Solving
-3.75 + x = -2.75

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -2.75 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -2.75 + 3.75
x = -2.75 + 3.75

Combine like terms: -2.75 + 3.75 = 1
x = 1

Simplifying
x = 1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.5, 1}

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