5565.13=5000(1+r)(1+r)

Solution for 5565.13=5000(1+r)(1+r) equation:

Simplifying
5565.13 = 5000(1 + r)(1 + r)

Multiply (1 + r) * (1 + r)
5565.13 = 5000(1(1 + r) + r(1 + r))
5565.13 = 5000((1 * 1 + r * 1) + r(1 + r))
5565.13 = 5000((1 + 1r) + r(1 + r))
5565.13 = 5000(1 + 1r + (1 * r + r * r))
5565.13 = 5000(1 + 1r + (1r + r2))

Combine like terms: 1r + 1r = 2r
5565.13 = 5000(1 + 2r + r2)
5565.13 = (1 * 5000 + 2r * 5000 + r2 * 5000)
5565.13 = (5000 + 10000r + 5000r2)

Solving
5565.13 = 5000 + 10000r + 5000r2

Solving for variable 'r'.

Combine like terms: 5565.13 + -5000 = 565.13
565.13 + -10000r + -5000r2 = 5000 + 10000r + 5000r2 + -5000 + -10000r + -5000r2

Reorder the terms:
565.13 + -10000r + -5000r2 = 5000 + -5000 + 10000r + -10000r + 5000r2 + -5000r2

Combine like terms: 5000 + -5000 = 0
565.13 + -10000r + -5000r2 = 0 + 10000r + -10000r + 5000r2 + -5000r2
565.13 + -10000r + -5000r2 = 10000r + -10000r + 5000r2 + -5000r2

Combine like terms: 10000r + -10000r = 0
565.13 + -10000r + -5000r2 = 0 + 5000r2 + -5000r2
565.13 + -10000r + -5000r2 = 5000r2 + -5000r2

Combine like terms: 5000r2 + -5000r2 = 0
565.13 + -10000r + -5000r2 = 0

Begin completing the square.  Divide all terms by
-5000 the coefficient of the squared term: 

Divide each side by '-5000'.
-0.113026 + 2r + r2 = 0

Move the constant term to the right:

Add '0.113026' to each side of the equation.
-0.113026 + 2r + 0.113026 + r2 = 0 + 0.113026

Reorder the terms:
-0.113026 + 0.113026 + 2r + r2 = 0 + 0.113026

Combine like terms: -0.113026 + 0.113026 = 0.000000
0.000000 + 2r + r2 = 0 + 0.113026
2r + r2 = 0 + 0.113026

Combine like terms: 0 + 0.113026 = 0.113026
2r + r2 = 0.113026

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 = 0.113026 + 1

Reorder the terms:
1 + 2r + r2 = 0.113026 + 1

Combine like terms: 0.113026 + 1 = 1.113026
1 + 2r + r2 = 1.113026

Factor a perfect square on the left side:
(r + 1)(r + 1) = 1.113026

Calculate the square root of the right side: 1.055000474

Break this problem into two subproblems by setting 
(r + 1) equal to 1.055000474 and -1.055000474.

Subproblem 1
r + 1 = 1.055000474

Simplifying
r + 1 = 1.055000474

Reorder the terms:
1 + r = 1.055000474

Solving
1 + r = 1.055000474

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 = 1.055000474 + -1

Combine like terms: 1 + -1 = 0
0 + r = 1.055000474 + -1
r = 1.055000474 + -1

Combine like terms: 1.055000474 + -1 = 0.055000474
r = 0.055000474

Simplifying
r = 0.055000474

Subproblem 2
r + 1 = -1.055000474

Simplifying
r + 1 = -1.055000474

Reorder the terms:
1 + r = -1.055000474

Solving
1 + r = -1.055000474

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 = -1.055000474 + -1

Combine like terms: 1 + -1 = 0
0 + r = -1.055000474 + -1
r = -1.055000474 + -1

Combine like terms: -1.055000474 + -1 = -2.055000474
r = -2.055000474

Simplifying
r = -2.055000474

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.055000474, -2.055000474}