7k^2-14k-96=0

Solution for 7k^2-14k-96=0 equation:

Simplifying
7k2 + -14k + -96 = 0

Reorder the terms:
-96 + -14k + 7k2 = 0

Solving
-96 + -14k + 7k2 = 0

Solving for variable 'k'.

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

Divide each side by '7'.
-13.71428571 + -2k + k2 = 0

Move the constant term to the right:

Add '13.71428571' to each side of the equation.
-13.71428571 + -2k + 13.71428571 + k2 = 0 + 13.71428571

Reorder the terms:
-13.71428571 + 13.71428571 + -2k + k2 = 0 + 13.71428571

Combine like terms: -13.71428571 + 13.71428571 = 0.00000000
0.00000000 + -2k + k2 = 0 + 13.71428571
-2k + k2 = 0 + 13.71428571

Combine like terms: 0 + 13.71428571 = 13.71428571
-2k + k2 = 13.71428571

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 = 13.71428571 + 1

Reorder the terms:
1 + -2k + k2 = 13.71428571 + 1

Combine like terms: 13.71428571 + 1 = 14.71428571
1 + -2k + k2 = 14.71428571

Factor a perfect square on the left side:
(k + -1)(k + -1) = 14.71428571

Calculate the square root of the right side: 3.835920451

Break this problem into two subproblems by setting 
(k + -1) equal to 3.835920451 and -3.835920451.

Subproblem 1
k + -1 = 3.835920451

Simplifying
k + -1 = 3.835920451

Reorder the terms:
-1 + k = 3.835920451

Solving
-1 + k = 3.835920451

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 = 3.835920451 + 1

Combine like terms: -1 + 1 = 0
0 + k = 3.835920451 + 1
k = 3.835920451 + 1

Combine like terms: 3.835920451 + 1 = 4.835920451
k = 4.835920451

Simplifying
k = 4.835920451

Subproblem 2
k + -1 = -3.835920451

Simplifying
k + -1 = -3.835920451

Reorder the terms:
-1 + k = -3.835920451

Solving
-1 + k = -3.835920451

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 = -3.835920451 + 1

Combine like terms: -1 + 1 = 0
0 + k = -3.835920451 + 1
k = -3.835920451 + 1

Combine like terms: -3.835920451 + 1 = -2.835920451
k = -2.835920451

Simplifying
k = -2.835920451

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.835920451, -2.835920451}