k^2+10k-13=0

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Solution for k^2+10k-13=0 equation: 


Simplifying
k2 + 10k + -13 = 0

Reorder the terms:
-13 + 10k + k2 = 0

Solving
-13 + 10k + 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 + 10k + 13 + k2 = 0 + 13

Reorder the terms:
-13 + 13 + 10k + k2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 10k + k2 = 0 + 13
10k + k2 = 0 + 13

Combine like terms: 0 + 13 = 13
10k + k2 = 13

The k term is 10k.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10k + 25 + k2 = 13 + 25

Reorder the terms:
25 + 10k + k2 = 13 + 25

Combine like terms: 13 + 25 = 38
25 + 10k + k2 = 38

Factor a perfect square on the left side:
(k + 5)(k + 5) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(k + 5) equal to 6.164414003 and -6.164414003.


Subproblem 1
k + 5 = 6.164414003

Simplifying
k + 5 = 6.164414003

Reorder the terms:
5 + k = 6.164414003

Solving
5 + k = 6.164414003

Solving for variable 'k'.

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

Add '-5' to each side of the equation.
5 + -5 + k = 6.164414003 + -5

Combine like terms: 5 + -5 = 0
0 + k = 6.164414003 + -5
k = 6.164414003 + -5

Combine like terms: 6.164414003 + -5 = 1.164414003
k = 1.164414003

Simplifying
k = 1.164414003


Subproblem 2
k + 5 = -6.164414003

Simplifying
k + 5 = -6.164414003

Reorder the terms:
5 + k = -6.164414003

Solving
5 + k = -6.164414003

Solving for variable 'k'.

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

Add '-5' to each side of the equation.
5 + -5 + k = -6.164414003 + -5

Combine like terms: 5 + -5 = 0
0 + k = -6.164414003 + -5
k = -6.164414003 + -5

Combine like terms: -6.164414003 + -5 = -11.164414003
k = -11.164414003

Simplifying
k = -11.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.164414003, -11.164414003}

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