2k^2-4k-9-18=0

Solution for 2k^2-4k-9-18=0 equation:

Simplifying
2k2 + -4k + -9 + -18 = 0

Reorder the terms:
-9 + -18 + -4k + 2k2 = 0

Combine like terms: -9 + -18 = -27
-27 + -4k + 2k2 = 0

Solving
-27 + -4k + 2k2 = 0

Solving for variable 'k'.

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

Divide each side by '2'.
-13.5 + -2k + k2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -2k + 13.5 + k2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -2k + k2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -2k + k2 = 0 + 13.5
-2k + k2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-2k + k2 = 13.5

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = 13.5 + 1

Reorder the terms:
1 + -2k + k2 = 13.5 + 1

Combine like terms: 13.5 + 1 = 14.5
1 + -2k + k2 = 14.5

Factor a perfect square on the left side:
(k + -1)(k + -1) = 14.5

Calculate the square root of the right side: 3.807886553

Break this problem into two subproblems by setting 
(k + -1) equal to 3.807886553 and -3.807886553.

Subproblem 1
k + -1 = 3.807886553

Simplifying
k + -1 = 3.807886553

Reorder the terms:
-1 + k = 3.807886553

Solving
-1 + k = 3.807886553

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 3.807886553 + 1

Combine like terms: -1 + 1 = 0
0 + k = 3.807886553 + 1
k = 3.807886553 + 1

Combine like terms: 3.807886553 + 1 = 4.807886553
k = 4.807886553

Simplifying
k = 4.807886553

Subproblem 2
k + -1 = -3.807886553

Simplifying
k + -1 = -3.807886553

Reorder the terms:
-1 + k = -3.807886553

Solving
-1 + k = -3.807886553

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -3.807886553 + 1

Combine like terms: -1 + 1 = 0
0 + k = -3.807886553 + 1
k = -3.807886553 + 1

Combine like terms: -3.807886553 + 1 = -2.807886553
k = -2.807886553

Simplifying
k = -2.807886553

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.807886553, -2.807886553}