(k+5)(k+5)=15

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Solution for (k+5)(k+5)=15 equation: 


Simplifying
(k + 5)(k + 5) = 15

Reorder the terms:
(5 + k)(k + 5) = 15

Reorder the terms:
(5 + k)(5 + k) = 15

Multiply (5 + k) * (5 + k)
(5(5 + k) + k(5 + k)) = 15
((5 * 5 + k * 5) + k(5 + k)) = 15
((25 + 5k) + k(5 + k)) = 15
(25 + 5k + (5 * k + k * k)) = 15
(25 + 5k + (5k + k2)) = 15

Combine like terms: 5k + 5k = 10k
(25 + 10k + k2) = 15

Solving
25 + 10k + k2 = 15

Solving for variable 'k'.

Reorder the terms:
25 + -15 + 10k + k2 = 15 + -15

Combine like terms: 25 + -15 = 10
10 + 10k + k2 = 15 + -15

Combine like terms: 15 + -15 = 0
10 + 10k + k2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -10 + 25

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

Combine like terms: -10 + 25 = 15
25 + 10k + k2 = 15

Factor a perfect square on the left side:
(k + 5)(k + 5) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(k + 5) equal to 3.872983346 and -3.872983346.


Subproblem 1
k + 5 = 3.872983346

Simplifying
k + 5 = 3.872983346

Reorder the terms:
5 + k = 3.872983346

Solving
5 + k = 3.872983346

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 = 3.872983346 + -5

Combine like terms: 5 + -5 = 0
0 + k = 3.872983346 + -5
k = 3.872983346 + -5

Combine like terms: 3.872983346 + -5 = -1.127016654
k = -1.127016654

Simplifying
k = -1.127016654


Subproblem 2
k + 5 = -3.872983346

Simplifying
k + 5 = -3.872983346

Reorder the terms:
5 + k = -3.872983346

Solving
5 + k = -3.872983346

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 = -3.872983346 + -5

Combine like terms: 5 + -5 = 0
0 + k = -3.872983346 + -5
k = -3.872983346 + -5

Combine like terms: -3.872983346 + -5 = -8.872983346
k = -8.872983346

Simplifying
k = -8.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-1.127016654, -8.872983346}

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