7k^2+14k-65=6

Solution for 7k^2+14k-65=6 equation:

Simplifying
7k2 + 14k + -65 = 6

Reorder the terms:
-65 + 14k + 7k2 = 6

Solving
-65 + 14k + 7k2 = 6

Solving for variable 'k'.

Reorder the terms:
-65 + -6 + 14k + 7k2 = 6 + -6

Combine like terms: -65 + -6 = -71
-71 + 14k + 7k2 = 6 + -6

Combine like terms: 6 + -6 = 0
-71 + 14k + 7k2 = 0

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

Divide each side by '7'.
-10.14285714 + 2k + k2 = 0

Move the constant term to the right:

Add '10.14285714' to each side of the equation.
-10.14285714 + 2k + 10.14285714 + k2 = 0 + 10.14285714

Reorder the terms:
-10.14285714 + 10.14285714 + 2k + k2 = 0 + 10.14285714

Combine like terms: -10.14285714 + 10.14285714 = 0.00000000
0.00000000 + 2k + k2 = 0 + 10.14285714
2k + k2 = 0 + 10.14285714

Combine like terms: 0 + 10.14285714 = 10.14285714
2k + k2 = 10.14285714

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 = 10.14285714 + 1

Reorder the terms:
1 + 2k + k2 = 10.14285714 + 1

Combine like terms: 10.14285714 + 1 = 11.14285714
1 + 2k + k2 = 11.14285714

Factor a perfect square on the left side:
(k + 1)(k + 1) = 11.14285714

Calculate the square root of the right side: 3.338091841

Break this problem into two subproblems by setting 
(k + 1) equal to 3.338091841 and -3.338091841.

Subproblem 1
k + 1 = 3.338091841

Simplifying
k + 1 = 3.338091841

Reorder the terms:
1 + k = 3.338091841

Solving
1 + k = 3.338091841

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 = 3.338091841 + -1

Combine like terms: 1 + -1 = 0
0 + k = 3.338091841 + -1
k = 3.338091841 + -1

Combine like terms: 3.338091841 + -1 = 2.338091841
k = 2.338091841

Simplifying
k = 2.338091841

Subproblem 2
k + 1 = -3.338091841

Simplifying
k + 1 = -3.338091841

Reorder the terms:
1 + k = -3.338091841

Solving
1 + k = -3.338091841

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 = -3.338091841 + -1

Combine like terms: 1 + -1 = 0
0 + k = -3.338091841 + -1
k = -3.338091841 + -1

Combine like terms: -3.338091841 + -1 = -4.338091841
k = -4.338091841

Simplifying
k = -4.338091841

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.338091841, -4.338091841}