2k(k+5)=5

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Solution for 2k(k+5)=5 equation: 


Simplifying
2k(k + 5) = 5

Reorder the terms:
2k(5 + k) = 5
(5 * 2k + k * 2k) = 5
(10k + 2k2) = 5

Solving
10k + 2k2 = 5

Solving for variable 'k'.

Reorder the terms:
-5 + 10k + 2k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 10k + 2k2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-2.5 + 5k + k2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 5k + 2.5 + k2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 5k + k2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 5k + k2 = 0 + 2.5
5k + k2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
5k + k2 = 2.5

The k term is 5k.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5k + 6.25 + k2 = 2.5 + 6.25

Reorder the terms:
6.25 + 5k + k2 = 2.5 + 6.25

Combine like terms: 2.5 + 6.25 = 8.75
6.25 + 5k + k2 = 8.75

Factor a perfect square on the left side:
(k + 2.5)(k + 2.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(k + 2.5) equal to 2.958039892 and -2.958039892.


Subproblem 1
k + 2.5 = 2.958039892

Simplifying
k + 2.5 = 2.958039892

Reorder the terms:
2.5 + k = 2.958039892

Solving
2.5 + k = 2.958039892

Solving for variable 'k'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + k = 2.958039892 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = 2.958039892 + -2.5
k = 2.958039892 + -2.5

Combine like terms: 2.958039892 + -2.5 = 0.458039892
k = 0.458039892

Simplifying
k = 0.458039892


Subproblem 2
k + 2.5 = -2.958039892

Simplifying
k + 2.5 = -2.958039892

Reorder the terms:
2.5 + k = -2.958039892

Solving
2.5 + k = -2.958039892

Solving for variable 'k'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + k = -2.958039892 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = -2.958039892 + -2.5
k = -2.958039892 + -2.5

Combine like terms: -2.958039892 + -2.5 = -5.458039892
k = -5.458039892

Simplifying
k = -5.458039892


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.458039892, -5.458039892}

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