k^2-11k+2=0

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Solution for k^2-11k+2=0 equation: 


Simplifying
k2 + -11k + 2 = 0

Reorder the terms:
2 + -11k + k2 = 0

Solving
2 + -11k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -11k + -2 + k2 = 0 + -2

Reorder the terms:
2 + -2 + -11k + k2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -11k + k2 = 0 + -2
-11k + k2 = 0 + -2

Combine like terms: 0 + -2 = -2
-11k + k2 = -2

The k term is -11k.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11k + 30.25 + k2 = -2 + 30.25

Reorder the terms:
30.25 + -11k + k2 = -2 + 30.25

Combine like terms: -2 + 30.25 = 28.25
30.25 + -11k + k2 = 28.25

Factor a perfect square on the left side:
(k + -5.5)(k + -5.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(k + -5.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
k + -5.5 = 5.315072906

Simplifying
k + -5.5 = 5.315072906

Reorder the terms:
-5.5 + k = 5.315072906

Solving
-5.5 + k = 5.315072906

Solving for variable 'k'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + k = 5.315072906 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + k = 5.315072906 + 5.5
k = 5.315072906 + 5.5

Combine like terms: 5.315072906 + 5.5 = 10.815072906
k = 10.815072906

Simplifying
k = 10.815072906


Subproblem 2
k + -5.5 = -5.315072906

Simplifying
k + -5.5 = -5.315072906

Reorder the terms:
-5.5 + k = -5.315072906

Solving
-5.5 + k = -5.315072906

Solving for variable 'k'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + k = -5.315072906 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + k = -5.315072906 + 5.5
k = -5.315072906 + 5.5

Combine like terms: -5.315072906 + 5.5 = 0.184927094
k = 0.184927094

Simplifying
k = 0.184927094


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {10.815072906, 0.184927094}

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