k^2-8k-23=0

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Solution for k^2-8k-23=0 equation:


Simplifying
k2 + -8k + -23 = 0

Reorder the terms:
-23 + -8k + k2 = 0

Solving
-23 + -8k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -8k + 23 + k2 = 0 + 23

Reorder the terms:
-23 + 23 + -8k + k2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -8k + k2 = 0 + 23
-8k + k2 = 0 + 23

Combine like terms: 0 + 23 = 23
-8k + k2 = 23

The k term is -8k.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8k + 16 + k2 = 23 + 16

Reorder the terms:
16 + -8k + k2 = 23 + 16

Combine like terms: 23 + 16 = 39
16 + -8k + k2 = 39

Factor a perfect square on the left side:
(k + -4)(k + -4) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(k + -4) equal to 6.244997998 and -6.244997998.


Subproblem 1
k + -4 = 6.244997998

Simplifying
k + -4 = 6.244997998

Reorder the terms:
-4 + k = 6.244997998

Solving
-4 + k = 6.244997998

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + k = 6.244997998 + 4

Combine like terms: -4 + 4 = 0
0 + k = 6.244997998 + 4
k = 6.244997998 + 4

Combine like terms: 6.244997998 + 4 = 10.244997998
k = 10.244997998

Simplifying
k = 10.244997998


Subproblem 2
k + -4 = -6.244997998

Simplifying
k + -4 = -6.244997998

Reorder the terms:
-4 + k = -6.244997998

Solving
-4 + k = -6.244997998

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + k = -6.244997998 + 4

Combine like terms: -4 + 4 = 0
0 + k = -6.244997998 + 4
k = -6.244997998 + 4

Combine like terms: -6.244997998 + 4 = -2.244997998
k = -2.244997998

Simplifying
k = -2.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {10.244997998, -2.244997998}

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