7k^2-28k-48=0

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Solution for 7k^2-28k-48=0 equation: 


Simplifying
7k2 + -28k + -48 = 0

Reorder the terms:
-48 + -28k + 7k2 = 0

Solving
-48 + -28k + 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'.
-6.857142857 + -4k + k2 = 0

Move the constant term to the right:

Add '6.857142857' to each side of the equation.
-6.857142857 + -4k + 6.857142857 + k2 = 0 + 6.857142857

Reorder the terms:
-6.857142857 + 6.857142857 + -4k + k2 = 0 + 6.857142857

Combine like terms: -6.857142857 + 6.857142857 = 0.000000000
0.000000000 + -4k + k2 = 0 + 6.857142857
-4k + k2 = 0 + 6.857142857

Combine like terms: 0 + 6.857142857 = 6.857142857
-4k + k2 = 6.857142857

The k term is -4k.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4k + 4 + k2 = 6.857142857 + 4

Reorder the terms:
4 + -4k + k2 = 6.857142857 + 4

Combine like terms: 6.857142857 + 4 = 10.857142857
4 + -4k + k2 = 10.857142857

Factor a perfect square on the left side:
(k + -2)(k + -2) = 10.857142857

Calculate the square root of the right side: 3.295017884

Break this problem into two subproblems by setting 
(k + -2) equal to 3.295017884 and -3.295017884.


Subproblem 1
k + -2 = 3.295017884

Simplifying
k + -2 = 3.295017884

Reorder the terms:
-2 + k = 3.295017884

Solving
-2 + k = 3.295017884

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = 3.295017884 + 2

Combine like terms: -2 + 2 = 0
0 + k = 3.295017884 + 2
k = 3.295017884 + 2

Combine like terms: 3.295017884 + 2 = 5.295017884
k = 5.295017884

Simplifying
k = 5.295017884


Subproblem 2
k + -2 = -3.295017884

Simplifying
k + -2 = -3.295017884

Reorder the terms:
-2 + k = -3.295017884

Solving
-2 + k = -3.295017884

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = -3.295017884 + 2

Combine like terms: -2 + 2 = 0
0 + k = -3.295017884 + 2
k = -3.295017884 + 2

Combine like terms: -3.295017884 + 2 = -1.295017884
k = -1.295017884

Simplifying
k = -1.295017884


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {5.295017884, -1.295017884}

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