k^2-10k-54=0

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Solution for k^2-10k-54=0 equation: 


Simplifying
k2 + -10k + -54 = 0

Reorder the terms:
-54 + -10k + k2 = 0

Solving
-54 + -10k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -10k + 54 + k2 = 0 + 54

Reorder the terms:
-54 + 54 + -10k + k2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -10k + k2 = 0 + 54
-10k + k2 = 0 + 54

Combine like terms: 0 + 54 = 54
-10k + k2 = 54

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 = 54 + 25

Reorder the terms:
25 + -10k + k2 = 54 + 25

Combine like terms: 54 + 25 = 79
25 + -10k + k2 = 79

Factor a perfect square on the left side:
(k + -5)(k + -5) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(k + -5) equal to 8.888194417 and -8.888194417.


Subproblem 1
k + -5 = 8.888194417

Simplifying
k + -5 = 8.888194417

Reorder the terms:
-5 + k = 8.888194417

Solving
-5 + k = 8.888194417

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 = 8.888194417 + 5

Combine like terms: -5 + 5 = 0
0 + k = 8.888194417 + 5
k = 8.888194417 + 5

Combine like terms: 8.888194417 + 5 = 13.888194417
k = 13.888194417

Simplifying
k = 13.888194417


Subproblem 2
k + -5 = -8.888194417

Simplifying
k + -5 = -8.888194417

Reorder the terms:
-5 + k = -8.888194417

Solving
-5 + k = -8.888194417

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 = -8.888194417 + 5

Combine like terms: -5 + 5 = 0
0 + k = -8.888194417 + 5
k = -8.888194417 + 5

Combine like terms: -8.888194417 + 5 = -3.888194417
k = -3.888194417

Simplifying
k = -3.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {13.888194417, -3.888194417}

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