k^2+26k+19=0

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Solution for k^2+26k+19=0 equation:


Simplifying
k2 + 26k + 19 = 0

Reorder the terms:
19 + 26k + k2 = 0

Solving
19 + 26k + 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 + 26k + -19 + k2 = 0 + -19

Reorder the terms:
19 + -19 + 26k + k2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 26k + k2 = 0 + -19
26k + k2 = 0 + -19

Combine like terms: 0 + -19 = -19
26k + k2 = -19

The k term is 26k.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26k + 169 + k2 = -19 + 169

Reorder the terms:
169 + 26k + k2 = -19 + 169

Combine like terms: -19 + 169 = 150
169 + 26k + k2 = 150

Factor a perfect square on the left side:
(k + 13)(k + 13) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(k + 13) equal to 12.247448714 and -12.247448714.


Subproblem 1
k + 13 = 12.247448714

Simplifying
k + 13 = 12.247448714

Reorder the terms:
13 + k = 12.247448714

Solving
13 + k = 12.247448714

Solving for variable 'k'.

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

Add '-13' to each side of the equation.
13 + -13 + k = 12.247448714 + -13

Combine like terms: 13 + -13 = 0
0 + k = 12.247448714 + -13
k = 12.247448714 + -13

Combine like terms: 12.247448714 + -13 = -0.752551286
k = -0.752551286

Simplifying
k = -0.752551286


Subproblem 2
k + 13 = -12.247448714

Simplifying
k + 13 = -12.247448714

Reorder the terms:
13 + k = -12.247448714

Solving
13 + k = -12.247448714

Solving for variable 'k'.

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

Add '-13' to each side of the equation.
13 + -13 + k = -12.247448714 + -13

Combine like terms: 13 + -13 = 0
0 + k = -12.247448714 + -13
k = -12.247448714 + -13

Combine like terms: -12.247448714 + -13 = -25.247448714
k = -25.247448714

Simplifying
k = -25.247448714


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.752551286, -25.247448714}

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