2k^2+41k-9=0

Solution for 2k^2+41k-9=0 equation:

Simplifying
2k2 + 41k + -9 = 0

Reorder the terms:
-9 + 41k + 2k2 = 0

Solving
-9 + 41k + 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'.
-4.5 + 20.5k + k2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 20.5k + 4.5 + k2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 20.5k + k2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 20.5k + k2 = 0 + 4.5
20.5k + k2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
20.5k + k2 = 4.5

The k term is 20.5k.  Take half its coefficient (10.25).
Square it (105.0625) and add it to both sides.

Add '105.0625' to each side of the equation.
20.5k + 105.0625 + k2 = 4.5 + 105.0625

Reorder the terms:
105.0625 + 20.5k + k2 = 4.5 + 105.0625

Combine like terms: 4.5 + 105.0625 = 109.5625
105.0625 + 20.5k + k2 = 109.5625

Factor a perfect square on the left side:
(k + 10.25)(k + 10.25) = 109.5625

Calculate the square root of the right side: 10.467210708

Break this problem into two subproblems by setting 
(k + 10.25) equal to 10.467210708 and -10.467210708.

Subproblem 1
k + 10.25 = 10.467210708

Simplifying
k + 10.25 = 10.467210708

Reorder the terms:
10.25 + k = 10.467210708

Solving
10.25 + k = 10.467210708

Solving for variable 'k'.

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

Add '-10.25' to each side of the equation.
10.25 + -10.25 + k = 10.467210708 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + k = 10.467210708 + -10.25
k = 10.467210708 + -10.25

Combine like terms: 10.467210708 + -10.25 = 0.217210708
k = 0.217210708

Simplifying
k = 0.217210708

Subproblem 2
k + 10.25 = -10.467210708

Simplifying
k + 10.25 = -10.467210708

Reorder the terms:
10.25 + k = -10.467210708

Solving
10.25 + k = -10.467210708

Solving for variable 'k'.

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

Add '-10.25' to each side of the equation.
10.25 + -10.25 + k = -10.467210708 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + k = -10.467210708 + -10.25
k = -10.467210708 + -10.25

Combine like terms: -10.467210708 + -10.25 = -20.717210708
k = -20.717210708

Simplifying
k = -20.717210708

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.217210708, -20.717210708}