12.666666-9x+x^2=0

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Solution for 12.666666-9x+x^2=0 equation: 


Simplifying
12.666666 + -9x + x2 = 0

Solving
12.666666 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-12.666666' to each side of the equation.
12.666666 + -9x + -12.666666 + x2 = 0 + -12.666666

Reorder the terms:
12.666666 + -12.666666 + -9x + x2 = 0 + -12.666666

Combine like terms: 12.666666 + -12.666666 = 0.000000
0.000000 + -9x + x2 = 0 + -12.666666
-9x + x2 = 0 + -12.666666

Combine like terms: 0 + -12.666666 = -12.666666
-9x + x2 = -12.666666

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 = -12.666666 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -12.666666 + 20.25

Combine like terms: -12.666666 + 20.25 = 7.583334
20.25 + -9x + x2 = 7.583334

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 7.583334

Calculate the square root of the right side: 2.753785395

Break this problem into two subproblems by setting 
(x + -4.5) equal to 2.753785395 and -2.753785395.


Subproblem 1
x + -4.5 = 2.753785395

Simplifying
x + -4.5 = 2.753785395

Reorder the terms:
-4.5 + x = 2.753785395

Solving
-4.5 + x = 2.753785395

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 = 2.753785395 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 2.753785395 + 4.5
x = 2.753785395 + 4.5

Combine like terms: 2.753785395 + 4.5 = 7.253785395
x = 7.253785395

Simplifying
x = 7.253785395


Subproblem 2
x + -4.5 = -2.753785395

Simplifying
x + -4.5 = -2.753785395

Reorder the terms:
-4.5 + x = -2.753785395

Solving
-4.5 + x = -2.753785395

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 = -2.753785395 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -2.753785395 + 4.5
x = -2.753785395 + 4.5

Combine like terms: -2.753785395 + 4.5 = 1.746214605
x = 1.746214605

Simplifying
x = 1.746214605


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.253785395, 1.746214605}

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