(r+4)(r+4)=15

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Solution for (r+4)(r+4)=15 equation: 


Simplifying
(r + 4)(r + 4) = 15

Reorder the terms:
(4 + r)(r + 4) = 15

Reorder the terms:
(4 + r)(4 + r) = 15

Multiply (4 + r) * (4 + r)
(4(4 + r) + r(4 + r)) = 15
((4 * 4 + r * 4) + r(4 + r)) = 15
((16 + 4r) + r(4 + r)) = 15
(16 + 4r + (4 * r + r * r)) = 15
(16 + 4r + (4r + r2)) = 15

Combine like terms: 4r + 4r = 8r
(16 + 8r + r2) = 15

Solving
16 + 8r + r2 = 15

Solving for variable 'r'.

Reorder the terms:
16 + -15 + 8r + r2 = 15 + -15

Combine like terms: 16 + -15 = 1
1 + 8r + r2 = 15 + -15

Combine like terms: 15 + -15 = 0
1 + 8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 8r + -1 + r2 = 0 + -1

Reorder the terms:
1 + -1 + 8r + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8r + r2 = 0 + -1
8r + r2 = 0 + -1

Combine like terms: 0 + -1 = -1
8r + r2 = -1

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

Add '16' to each side of the equation.
8r + 16 + r2 = -1 + 16

Reorder the terms:
16 + 8r + r2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + 8r + r2 = 15

Factor a perfect square on the left side:
(r + 4)(r + 4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(r + 4) equal to 3.872983346 and -3.872983346.


Subproblem 1
r + 4 = 3.872983346

Simplifying
r + 4 = 3.872983346

Reorder the terms:
4 + r = 3.872983346

Solving
4 + r = 3.872983346

Solving for variable 'r'.

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

Add '-4' to each side of the equation.
4 + -4 + r = 3.872983346 + -4

Combine like terms: 4 + -4 = 0
0 + r = 3.872983346 + -4
r = 3.872983346 + -4

Combine like terms: 3.872983346 + -4 = -0.127016654
r = -0.127016654

Simplifying
r = -0.127016654


Subproblem 2
r + 4 = -3.872983346

Simplifying
r + 4 = -3.872983346

Reorder the terms:
4 + r = -3.872983346

Solving
4 + r = -3.872983346

Solving for variable 'r'.

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

Add '-4' to each side of the equation.
4 + -4 + r = -3.872983346 + -4

Combine like terms: 4 + -4 = 0
0 + r = -3.872983346 + -4
r = -3.872983346 + -4

Combine like terms: -3.872983346 + -4 = -7.872983346
r = -7.872983346

Simplifying
r = -7.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.127016654, -7.872983346}

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