2k^2+6k-1=0

Solution for 2k^2+6k-1=0 equation:

Simplifying
2k2 + 6k + -1 = 0

Reorder the terms:
-1 + 6k + 2k2 = 0

Solving
-1 + 6k + 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'.
-0.5 + 3k + k2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3k + 0.5 + k2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3k + k2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3k + k2 = 0 + 0.5
3k + k2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3k + k2 = 0.5

The k term is 3k.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3k + 2.25 + k2 = 0.5 + 2.25

Reorder the terms:
2.25 + 3k + k2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + 3k + k2 = 2.75

Factor a perfect square on the left side:
(k + 1.5)(k + 1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(k + 1.5) equal to 1.658312395 and -1.658312395.

Subproblem 1
k + 1.5 = 1.658312395

Simplifying
k + 1.5 = 1.658312395

Reorder the terms:
1.5 + k = 1.658312395

Solving
1.5 + k = 1.658312395

Solving for variable 'k'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + k = 1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + k = 1.658312395 + -1.5
k = 1.658312395 + -1.5

Combine like terms: 1.658312395 + -1.5 = 0.158312395
k = 0.158312395

Simplifying
k = 0.158312395

Subproblem 2
k + 1.5 = -1.658312395

Simplifying
k + 1.5 = -1.658312395

Reorder the terms:
1.5 + k = -1.658312395

Solving
1.5 + k = -1.658312395

Solving for variable 'k'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + k = -1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + k = -1.658312395 + -1.5
k = -1.658312395 + -1.5

Combine like terms: -1.658312395 + -1.5 = -3.158312395
k = -3.158312395

Simplifying
k = -3.158312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.158312395, -3.158312395}