4k(k+5)=5

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Solution for 4k(k+5)=5 equation: 


Simplifying
4k(k + 5) = 5

Reorder the terms:
4k(5 + k) = 5
(5 * 4k + k * 4k) = 5
(20k + 4k2) = 5

Solving
20k + 4k2 = 5

Solving for variable 'k'.

Reorder the terms:
-5 + 20k + 4k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 20k + 4k2 = 0

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

Divide each side by '4'.
-1.25 + 5k + k2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 5k + 1.25 + k2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 5k + k2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 5k + k2 = 0 + 1.25
5k + k2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
5k + k2 = 1.25

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 = 1.25 + 6.25

Reorder the terms:
6.25 + 5k + k2 = 1.25 + 6.25

Combine like terms: 1.25 + 6.25 = 7.5
6.25 + 5k + k2 = 7.5

Factor a perfect square on the left side:
(k + 2.5)(k + 2.5) = 7.5

Calculate the square root of the right side: 2.738612788

Break this problem into two subproblems by setting 
(k + 2.5) equal to 2.738612788 and -2.738612788.


Subproblem 1
k + 2.5 = 2.738612788

Simplifying
k + 2.5 = 2.738612788

Reorder the terms:
2.5 + k = 2.738612788

Solving
2.5 + k = 2.738612788

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 = 2.738612788 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = 2.738612788 + -2.5
k = 2.738612788 + -2.5

Combine like terms: 2.738612788 + -2.5 = 0.238612788
k = 0.238612788

Simplifying
k = 0.238612788


Subproblem 2
k + 2.5 = -2.738612788

Simplifying
k + 2.5 = -2.738612788

Reorder the terms:
2.5 + k = -2.738612788

Solving
2.5 + k = -2.738612788

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 = -2.738612788 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = -2.738612788 + -2.5
k = -2.738612788 + -2.5

Combine like terms: -2.738612788 + -2.5 = -5.238612788
k = -5.238612788

Simplifying
k = -5.238612788


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.238612788, -5.238612788}

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