5k^2-18k-26=13

Solution for 5k^2-18k-26=13 equation:

Simplifying
5k2 + -18k + -26 = 13

Reorder the terms:
-26 + -18k + 5k2 = 13

Solving
-26 + -18k + 5k2 = 13

Solving for variable 'k'.

Reorder the terms:
-26 + -13 + -18k + 5k2 = 13 + -13

Combine like terms: -26 + -13 = -39
-39 + -18k + 5k2 = 13 + -13

Combine like terms: 13 + -13 = 0
-39 + -18k + 5k2 = 0

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

Divide each side by '5'.
-7.8 + -3.6k + k2 = 0

Move the constant term to the right:

Add '7.8' to each side of the equation.
-7.8 + -3.6k + 7.8 + k2 = 0 + 7.8

Reorder the terms:
-7.8 + 7.8 + -3.6k + k2 = 0 + 7.8

Combine like terms: -7.8 + 7.8 = 0.0
0.0 + -3.6k + k2 = 0 + 7.8
-3.6k + k2 = 0 + 7.8

Combine like terms: 0 + 7.8 = 7.8
-3.6k + k2 = 7.8

The k term is -3.6k.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6k + 3.24 + k2 = 7.8 + 3.24

Reorder the terms:
3.24 + -3.6k + k2 = 7.8 + 3.24

Combine like terms: 7.8 + 3.24 = 11.04
3.24 + -3.6k + k2 = 11.04

Factor a perfect square on the left side:
(k + -1.8)(k + -1.8) = 11.04

Calculate the square root of the right side: 3.322649545

Break this problem into two subproblems by setting 
(k + -1.8) equal to 3.322649545 and -3.322649545.

Subproblem 1
k + -1.8 = 3.322649545

Simplifying
k + -1.8 = 3.322649545

Reorder the terms:
-1.8 + k = 3.322649545

Solving
-1.8 + k = 3.322649545

Solving for variable 'k'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + k = 3.322649545 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + k = 3.322649545 + 1.8
k = 3.322649545 + 1.8

Combine like terms: 3.322649545 + 1.8 = 5.122649545
k = 5.122649545

Simplifying
k = 5.122649545

Subproblem 2
k + -1.8 = -3.322649545

Simplifying
k + -1.8 = -3.322649545

Reorder the terms:
-1.8 + k = -3.322649545

Solving
-1.8 + k = -3.322649545

Solving for variable 'k'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + k = -3.322649545 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + k = -3.322649545 + 1.8
k = -3.322649545 + 1.8

Combine like terms: -3.322649545 + 1.8 = -1.522649545
k = -1.522649545

Simplifying
k = -1.522649545

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {5.122649545, -1.522649545}