c^2-12c+9=0

Solution for c^2-12c+9=0 equation:

Simplifying
c2 + -12c + 9 = 0

Reorder the terms:
9 + -12c + c2 = 0

Solving
9 + -12c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -12c + -9 + c2 = 0 + -9

Reorder the terms:
9 + -9 + -12c + c2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -12c + c2 = 0 + -9
-12c + c2 = 0 + -9

Combine like terms: 0 + -9 = -9
-12c + c2 = -9

The c term is -12c.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12c + 36 + c2 = -9 + 36

Reorder the terms:
36 + -12c + c2 = -9 + 36

Combine like terms: -9 + 36 = 27
36 + -12c + c2 = 27

Factor a perfect square on the left side:
(c + -6)(c + -6) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(c + -6) equal to 5.196152423 and -5.196152423.

Subproblem 1
c + -6 = 5.196152423

Simplifying
c + -6 = 5.196152423

Reorder the terms:
-6 + c = 5.196152423

Solving
-6 + c = 5.196152423

Solving for variable 'c'.

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

Add '6' to each side of the equation.
-6 + 6 + c = 5.196152423 + 6

Combine like terms: -6 + 6 = 0
0 + c = 5.196152423 + 6
c = 5.196152423 + 6

Combine like terms: 5.196152423 + 6 = 11.196152423
c = 11.196152423

Simplifying
c = 11.196152423

Subproblem 2
c + -6 = -5.196152423

Simplifying
c + -6 = -5.196152423

Reorder the terms:
-6 + c = -5.196152423

Solving
-6 + c = -5.196152423

Solving for variable 'c'.

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

Add '6' to each side of the equation.
-6 + 6 + c = -5.196152423 + 6

Combine like terms: -6 + 6 = 0
0 + c = -5.196152423 + 6
c = -5.196152423 + 6

Combine like terms: -5.196152423 + 6 = 0.803847577
c = 0.803847577

Simplifying
c = 0.803847577

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {11.196152423, 0.803847577}