9x-x^2=19.8

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Solution for 9x-x^2=19.8 equation: 


Simplifying
9x + -1x2 = 19.8

Solving
9x + -1x2 = 19.8

Solving for variable 'x'.

Reorder the terms:
-19.8 + 9x + -1x2 = 19.8 + -19.8

Combine like terms: 19.8 + -19.8 = 0.0
-19.8 + 9x + -1x2 = 0.0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
19.8 + -9x + x2 = 0.0

Move the constant term to the right:

Add '-19.8' to each side of the equation.
19.8 + -9x + -19.8 + x2 = 0.0 + -19.8

Reorder the terms:
19.8 + -19.8 + -9x + x2 = 0.0 + -19.8

Combine like terms: 19.8 + -19.8 = 0.0
0.0 + -9x + x2 = 0.0 + -19.8
-9x + x2 = 0.0 + -19.8

Combine like terms: 0.0 + -19.8 = -19.8
-9x + x2 = -19.8

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -19.8 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -19.8 + 20.25

Combine like terms: -19.8 + 20.25 = 0.45
20.25 + -9x + x2 = 0.45

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(x + -4.5) equal to 0.670820393 and -0.670820393.


Subproblem 1
x + -4.5 = 0.670820393

Simplifying
x + -4.5 = 0.670820393

Reorder the terms:
-4.5 + x = 0.670820393

Solving
-4.5 + x = 0.670820393

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 0.670820393 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 0.670820393 + 4.5
x = 0.670820393 + 4.5

Combine like terms: 0.670820393 + 4.5 = 5.170820393
x = 5.170820393

Simplifying
x = 5.170820393


Subproblem 2
x + -4.5 = -0.670820393

Simplifying
x + -4.5 = -0.670820393

Reorder the terms:
-4.5 + x = -0.670820393

Solving
-4.5 + x = -0.670820393

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -0.670820393 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -0.670820393 + 4.5
x = -0.670820393 + 4.5

Combine like terms: -0.670820393 + 4.5 = 3.829179607
x = 3.829179607

Simplifying
x = 3.829179607


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.170820393, 3.829179607}

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