k^2-18k+54=0

Solution for k^2-18k+54=0 equation:

Simplifying
k2 + -18k + 54 = 0

Reorder the terms:
54 + -18k + k2 = 0

Solving
54 + -18k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -18k + -54 + k2 = 0 + -54

Reorder the terms:
54 + -54 + -18k + k2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -18k + k2 = 0 + -54
-18k + k2 = 0 + -54

Combine like terms: 0 + -54 = -54
-18k + k2 = -54

The k term is -18k.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18k + 81 + k2 = -54 + 81

Reorder the terms:
81 + -18k + k2 = -54 + 81

Combine like terms: -54 + 81 = 27
81 + -18k + k2 = 27

Factor a perfect square on the left side:
(k + -9)(k + -9) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(k + -9) equal to 5.196152423 and -5.196152423.

Subproblem 1
k + -9 = 5.196152423

Simplifying
k + -9 = 5.196152423

Reorder the terms:
-9 + k = 5.196152423

Solving
-9 + k = 5.196152423

Solving for variable 'k'.

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

Add '9' to each side of the equation.
-9 + 9 + k = 5.196152423 + 9

Combine like terms: -9 + 9 = 0
0 + k = 5.196152423 + 9
k = 5.196152423 + 9

Combine like terms: 5.196152423 + 9 = 14.196152423
k = 14.196152423

Simplifying
k = 14.196152423

Subproblem 2
k + -9 = -5.196152423

Simplifying
k + -9 = -5.196152423

Reorder the terms:
-9 + k = -5.196152423

Solving
-9 + k = -5.196152423

Solving for variable 'k'.

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

Add '9' to each side of the equation.
-9 + 9 + k = -5.196152423 + 9

Combine like terms: -9 + 9 = 0
0 + k = -5.196152423 + 9
k = -5.196152423 + 9

Combine like terms: -5.196152423 + 9 = 3.803847577
k = 3.803847577

Simplifying
k = 3.803847577

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {14.196152423, 3.803847577}