(r+1)(r+1)=14

Solution for (r+1)(r+1)=14 equation:

Simplifying
(r + 1)(r + 1) = 14

Reorder the terms:
(1 + r)(r + 1) = 14

Reorder the terms:
(1 + r)(1 + r) = 14

Multiply (1 + r) * (1 + r)
(1(1 + r) + r(1 + r)) = 14
((1 * 1 + r * 1) + r(1 + r)) = 14
((1 + 1r) + r(1 + r)) = 14
(1 + 1r + (1 * r + r * r)) = 14
(1 + 1r + (1r + r2)) = 14

Combine like terms: 1r + 1r = 2r
(1 + 2r + r2) = 14

Solving
1 + 2r + r2 = 14

Solving for variable 'r'.

Reorder the terms:
1 + -14 + 2r + r2 = 14 + -14

Combine like terms: 1 + -14 = -13
-13 + 2r + r2 = 14 + -14

Combine like terms: 14 + -14 = 0
-13 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 2r + 13 + r2 = 0 + 13

Reorder the terms:
-13 + 13 + 2r + r2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 2r + r2 = 0 + 13
2r + r2 = 0 + 13

Combine like terms: 0 + 13 = 13
2r + r2 = 13

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 13 + 1

Reorder the terms:
1 + 2r + r2 = 13 + 1

Combine like terms: 13 + 1 = 14
1 + 2r + r2 = 14

Factor a perfect square on the left side:
(r + 1)(r + 1) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(r + 1) equal to 3.741657387 and -3.741657387.

Subproblem 1
r + 1 = 3.741657387

Simplifying
r + 1 = 3.741657387

Reorder the terms:
1 + r = 3.741657387

Solving
1 + r = 3.741657387

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = 3.741657387 + -1

Combine like terms: 1 + -1 = 0
0 + r = 3.741657387 + -1
r = 3.741657387 + -1

Combine like terms: 3.741657387 + -1 = 2.741657387
r = 2.741657387

Simplifying
r = 2.741657387

Subproblem 2
r + 1 = -3.741657387

Simplifying
r + 1 = -3.741657387

Reorder the terms:
1 + r = -3.741657387

Solving
1 + r = -3.741657387

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = -3.741657387 + -1

Combine like terms: 1 + -1 = 0
0 + r = -3.741657387 + -1
r = -3.741657387 + -1

Combine like terms: -3.741657387 + -1 = -4.741657387
r = -4.741657387

Simplifying
r = -4.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.741657387, -4.741657387}