-k^2+16k+28=0

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Solution for -k^2+16k+28=0 equation: 


Simplifying
-1k2 + 16k + 28 = 0

Reorder the terms:
28 + 16k + -1k2 = 0

Solving
28 + 16k + -1k2 = 0

Solving for variable 'k'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-28 + -16k + k2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -16k + 28 + k2 = 0 + 28

Reorder the terms:
-28 + 28 + -16k + k2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -16k + k2 = 0 + 28
-16k + k2 = 0 + 28

Combine like terms: 0 + 28 = 28
-16k + k2 = 28

The k term is -16k.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16k + 64 + k2 = 28 + 64

Reorder the terms:
64 + -16k + k2 = 28 + 64

Combine like terms: 28 + 64 = 92
64 + -16k + k2 = 92

Factor a perfect square on the left side:
(k + -8)(k + -8) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(k + -8) equal to 9.591663047 and -9.591663047.


Subproblem 1
k + -8 = 9.591663047

Simplifying
k + -8 = 9.591663047

Reorder the terms:
-8 + k = 9.591663047

Solving
-8 + k = 9.591663047

Solving for variable 'k'.

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

Add '8' to each side of the equation.
-8 + 8 + k = 9.591663047 + 8

Combine like terms: -8 + 8 = 0
0 + k = 9.591663047 + 8
k = 9.591663047 + 8

Combine like terms: 9.591663047 + 8 = 17.591663047
k = 17.591663047

Simplifying
k = 17.591663047


Subproblem 2
k + -8 = -9.591663047

Simplifying
k + -8 = -9.591663047

Reorder the terms:
-8 + k = -9.591663047

Solving
-8 + k = -9.591663047

Solving for variable 'k'.

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

Add '8' to each side of the equation.
-8 + 8 + k = -9.591663047 + 8

Combine like terms: -8 + 8 = 0
0 + k = -9.591663047 + 8
k = -9.591663047 + 8

Combine like terms: -9.591663047 + 8 = -1.591663047
k = -1.591663047

Simplifying
k = -1.591663047


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {17.591663047, -1.591663047}

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