x^2-6x+9=8.66667

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Solution for x^2-6x+9=8.66667 equation: 


Simplifying
x2 + -6x + 9 = 8.66667

Reorder the terms:
9 + -6x + x2 = 8.66667

Solving
9 + -6x + x2 = 8.66667

Solving for variable 'x'.

Reorder the terms:
9 + -8.66667 + -6x + x2 = 8.66667 + -8.66667

Combine like terms: 9 + -8.66667 = 0.33333
0.33333 + -6x + x2 = 8.66667 + -8.66667

Combine like terms: 8.66667 + -8.66667 = 0.00000
0.33333 + -6x + x2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '-0.33333' to each side of the equation.
0.33333 + -6x + -0.33333 + x2 = 0.00000 + -0.33333

Reorder the terms:
0.33333 + -0.33333 + -6x + x2 = 0.00000 + -0.33333

Combine like terms: 0.33333 + -0.33333 = 0.00000
0.00000 + -6x + x2 = 0.00000 + -0.33333
-6x + x2 = 0.00000 + -0.33333

Combine like terms: 0.00000 + -0.33333 = -0.33333
-6x + x2 = -0.33333

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -0.33333 + 9

Reorder the terms:
9 + -6x + x2 = -0.33333 + 9

Combine like terms: -0.33333 + 9 = 8.66667
9 + -6x + x2 = 8.66667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 8.66667

Calculate the square root of the right side: 2.943920855

Break this problem into two subproblems by setting 
(x + -3) equal to 2.943920855 and -2.943920855.


Subproblem 1
x + -3 = 2.943920855

Simplifying
x + -3 = 2.943920855

Reorder the terms:
-3 + x = 2.943920855

Solving
-3 + x = 2.943920855

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.943920855 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.943920855 + 3
x = 2.943920855 + 3

Combine like terms: 2.943920855 + 3 = 5.943920855
x = 5.943920855

Simplifying
x = 5.943920855


Subproblem 2
x + -3 = -2.943920855

Simplifying
x + -3 = -2.943920855

Reorder the terms:
-3 + x = -2.943920855

Solving
-3 + x = -2.943920855

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.943920855 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.943920855 + 3
x = -2.943920855 + 3

Combine like terms: -2.943920855 + 3 = 0.056079145
x = 0.056079145

Simplifying
x = 0.056079145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.943920855, 0.056079145}

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