2(k+7)-7(k-4)k=

Solution for 2(k+7)-7(k-4)k= equation:

Simplifying
2(k + 7) + -7(k + -4) * k = 0

Reorder the terms:
2(7 + k) + -7(k + -4) * k = 0
(7 * 2 + k * 2) + -7(k + -4) * k = 0
(14 + 2k) + -7(k + -4) * k = 0

Reorder the terms:
14 + 2k + -7(-4 + k) * k = 0

Reorder the terms for easier multiplication:
14 + 2k + -7k(-4 + k) = 0
14 + 2k + (-4 * -7k + k * -7k) = 0
14 + 2k + (28k + -7k2) = 0

Combine like terms: 2k + 28k = 30k
14 + 30k + -7k2 = 0

Solving
14 + 30k + -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'.
-2 + -4.285714286k + k2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4.285714286k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + -4.285714286k + k2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4.285714286k + k2 = 0 + 2
-4.285714286k + k2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4.285714286k + k2 = 2

The k term is -4.285714286k.  Take half its coefficient (-2.142857143).
Square it (4.591836735) and add it to both sides.

Add '4.591836735' to each side of the equation.
-4.285714286k + 4.591836735 + k2 = 2 + 4.591836735

Reorder the terms:
4.591836735 + -4.285714286k + k2 = 2 + 4.591836735

Combine like terms: 2 + 4.591836735 = 6.591836735
4.591836735 + -4.285714286k + k2 = 6.591836735

Factor a perfect square on the left side:
(k + -2.142857143)(k + -2.142857143) = 6.591836735

Calculate the square root of the right side: 2.567457251

Break this problem into two subproblems by setting 
(k + -2.142857143) equal to 2.567457251 and -2.567457251.

Subproblem 1
k + -2.142857143 = 2.567457251

Simplifying
k + -2.142857143 = 2.567457251

Reorder the terms:
-2.142857143 + k = 2.567457251

Solving
-2.142857143 + k = 2.567457251

Solving for variable 'k'.

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

Add '2.142857143' to each side of the equation.
-2.142857143 + 2.142857143 + k = 2.567457251 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + k = 2.567457251 + 2.142857143
k = 2.567457251 + 2.142857143

Combine like terms: 2.567457251 + 2.142857143 = 4.710314394
k = 4.710314394

Simplifying
k = 4.710314394

Subproblem 2
k + -2.142857143 = -2.567457251

Simplifying
k + -2.142857143 = -2.567457251

Reorder the terms:
-2.142857143 + k = -2.567457251

Solving
-2.142857143 + k = -2.567457251

Solving for variable 'k'.

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

Add '2.142857143' to each side of the equation.
-2.142857143 + 2.142857143 + k = -2.567457251 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + k = -2.567457251 + 2.142857143
k = -2.567457251 + 2.142857143

Combine like terms: -2.567457251 + 2.142857143 = -0.424600108
k = -0.424600108

Simplifying
k = -0.424600108

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.710314394, -0.424600108}