2.5=-0.2x(x-13.5)

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Solution for 2.5=-0.2x(x-13.5) equation: 


Simplifying
2.5 = -0.2x(x + -13.5)

Reorder the terms:
2.5 = -0.2x(-13.5 + x)
2.5 = (-13.5 * -0.2x + x * -0.2x)
2.5 = (2.7x + -0.2x2)

Solving
2.5 = 2.7x + -0.2x2

Solving for variable 'x'.

Reorder the terms:
2.5 + -2.7x + 0.2x2 = 2.7x + -2.7x + -0.2x2 + 0.2x2

Combine like terms: 2.7x + -2.7x = 0.0
2.5 + -2.7x + 0.2x2 = 0.0 + -0.2x2 + 0.2x2
2.5 + -2.7x + 0.2x2 = -0.2x2 + 0.2x2

Combine like terms: -0.2x2 + 0.2x2 = 0.0
2.5 + -2.7x + 0.2x2 = 0.0

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

Divide each side by '0.2'.
12.5 + -13.5x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + -13.5x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + -13.5x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + -13.5x + x2 = 0 + -12.5
-13.5x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
-13.5x + x2 = -12.5

The x term is -13.5x.  Take half its coefficient (-6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
-13.5x + 45.5625 + x2 = -12.5 + 45.5625

Reorder the terms:
45.5625 + -13.5x + x2 = -12.5 + 45.5625

Combine like terms: -12.5 + 45.5625 = 33.0625
45.5625 + -13.5x + x2 = 33.0625

Factor a perfect square on the left side:
(x + -6.75)(x + -6.75) = 33.0625

Calculate the square root of the right side: 5.75

Break this problem into two subproblems by setting 
(x + -6.75) equal to 5.75 and -5.75.


Subproblem 1
x + -6.75 = 5.75

Simplifying
x + -6.75 = 5.75

Reorder the terms:
-6.75 + x = 5.75

Solving
-6.75 + x = 5.75

Solving for variable 'x'.

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

Add '6.75' to each side of the equation.
-6.75 + 6.75 + x = 5.75 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + x = 5.75 + 6.75
x = 5.75 + 6.75

Combine like terms: 5.75 + 6.75 = 12.5
x = 12.5

Simplifying
x = 12.5


Subproblem 2
x + -6.75 = -5.75

Simplifying
x + -6.75 = -5.75

Reorder the terms:
-6.75 + x = -5.75

Solving
-6.75 + x = -5.75

Solving for variable 'x'.

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

Add '6.75' to each side of the equation.
-6.75 + 6.75 + x = -5.75 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + x = -5.75 + 6.75
x = -5.75 + 6.75

Combine like terms: -5.75 + 6.75 = 1
x = 1

Simplifying
x = 1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.5, 1}

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