k^2-10k-17=0

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Solution for k^2-10k-17=0 equation: 


Simplifying
k2 + -10k + -17 = 0

Reorder the terms:
-17 + -10k + k2 = 0

Solving
-17 + -10k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -10k + 17 + k2 = 0 + 17

Reorder the terms:
-17 + 17 + -10k + k2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -10k + k2 = 0 + 17
-10k + k2 = 0 + 17

Combine like terms: 0 + 17 = 17
-10k + k2 = 17

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 = 17 + 25

Reorder the terms:
25 + -10k + k2 = 17 + 25

Combine like terms: 17 + 25 = 42
25 + -10k + k2 = 42

Factor a perfect square on the left side:
(k + -5)(k + -5) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(k + -5) equal to 6.480740698 and -6.480740698.


Subproblem 1
k + -5 = 6.480740698

Simplifying
k + -5 = 6.480740698

Reorder the terms:
-5 + k = 6.480740698

Solving
-5 + k = 6.480740698

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 = 6.480740698 + 5

Combine like terms: -5 + 5 = 0
0 + k = 6.480740698 + 5
k = 6.480740698 + 5

Combine like terms: 6.480740698 + 5 = 11.480740698
k = 11.480740698

Simplifying
k = 11.480740698


Subproblem 2
k + -5 = -6.480740698

Simplifying
k + -5 = -6.480740698

Reorder the terms:
-5 + k = -6.480740698

Solving
-5 + k = -6.480740698

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 = -6.480740698 + 5

Combine like terms: -5 + 5 = 0
0 + k = -6.480740698 + 5
k = -6.480740698 + 5

Combine like terms: -6.480740698 + 5 = -1.480740698
k = -1.480740698

Simplifying
k = -1.480740698


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {11.480740698, -1.480740698}

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