k^2+16k-13=0

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Solution for k^2+16k-13=0 equation: 


Simplifying
k2 + 16k + -13 = 0

Reorder the terms:
-13 + 16k + k2 = 0

Solving
-13 + 16k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 16k + 13 + k2 = 0 + 13

Reorder the terms:
-13 + 13 + 16k + k2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 16k + k2 = 0 + 13
16k + k2 = 0 + 13

Combine like terms: 0 + 13 = 13
16k + k2 = 13

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 = 13 + 64

Reorder the terms:
64 + 16k + k2 = 13 + 64

Combine like terms: 13 + 64 = 77
64 + 16k + k2 = 77

Factor a perfect square on the left side:
(k + 8)(k + 8) = 77

Calculate the square root of the right side: 8.774964387

Break this problem into two subproblems by setting 
(k + 8) equal to 8.774964387 and -8.774964387.


Subproblem 1
k + 8 = 8.774964387

Simplifying
k + 8 = 8.774964387

Reorder the terms:
8 + k = 8.774964387

Solving
8 + k = 8.774964387

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 = 8.774964387 + -8

Combine like terms: 8 + -8 = 0
0 + k = 8.774964387 + -8
k = 8.774964387 + -8

Combine like terms: 8.774964387 + -8 = 0.774964387
k = 0.774964387

Simplifying
k = 0.774964387


Subproblem 2
k + 8 = -8.774964387

Simplifying
k + 8 = -8.774964387

Reorder the terms:
8 + k = -8.774964387

Solving
8 + k = -8.774964387

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 = -8.774964387 + -8

Combine like terms: 8 + -8 = 0
0 + k = -8.774964387 + -8
k = -8.774964387 + -8

Combine like terms: -8.774964387 + -8 = -16.774964387
k = -16.774964387

Simplifying
k = -16.774964387


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.774964387, -16.774964387}

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