k^2-14k-19=0

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Solution for k^2-14k-19=0 equation: 


Simplifying
k2 + -14k + -19 = 0

Reorder the terms:
-19 + -14k + k2 = 0

Solving
-19 + -14k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -14k + 19 + k2 = 0 + 19

Reorder the terms:
-19 + 19 + -14k + k2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -14k + k2 = 0 + 19
-14k + k2 = 0 + 19

Combine like terms: 0 + 19 = 19
-14k + k2 = 19

The k term is -14k.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14k + 49 + k2 = 19 + 49

Reorder the terms:
49 + -14k + k2 = 19 + 49

Combine like terms: 19 + 49 = 68
49 + -14k + k2 = 68

Factor a perfect square on the left side:
(k + -7)(k + -7) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(k + -7) equal to 8.246211251 and -8.246211251.


Subproblem 1
k + -7 = 8.246211251

Simplifying
k + -7 = 8.246211251

Reorder the terms:
-7 + k = 8.246211251

Solving
-7 + k = 8.246211251

Solving for variable 'k'.

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

Add '7' to each side of the equation.
-7 + 7 + k = 8.246211251 + 7

Combine like terms: -7 + 7 = 0
0 + k = 8.246211251 + 7
k = 8.246211251 + 7

Combine like terms: 8.246211251 + 7 = 15.246211251
k = 15.246211251

Simplifying
k = 15.246211251


Subproblem 2
k + -7 = -8.246211251

Simplifying
k + -7 = -8.246211251

Reorder the terms:
-7 + k = -8.246211251

Solving
-7 + k = -8.246211251

Solving for variable 'k'.

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

Add '7' to each side of the equation.
-7 + 7 + k = -8.246211251 + 7

Combine like terms: -7 + 7 = 0
0 + k = -8.246211251 + 7
k = -8.246211251 + 7

Combine like terms: -8.246211251 + 7 = -1.246211251
k = -1.246211251

Simplifying
k = -1.246211251


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {15.246211251, -1.246211251}

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