1000(1+r)(1+r)=1123.60

Solution for 1000(1+r)(1+r)=1123.60 equation:

Simplifying
1000(1 + r)(1 + r) = 1123.60

Multiply (1 + r) * (1 + r)
1000(1(1 + r) + r(1 + r)) = 1123.60
1000((1 * 1 + r * 1) + r(1 + r)) = 1123.60
1000((1 + 1r) + r(1 + r)) = 1123.60
1000(1 + 1r + (1 * r + r * r)) = 1123.60
1000(1 + 1r + (1r + r2)) = 1123.60

Combine like terms: 1r + 1r = 2r
1000(1 + 2r + r2) = 1123.60
(1 * 1000 + 2r * 1000 + r2 * 1000) = 1123.60
(1000 + 2000r + 1000r2) = 1123.60

Solving
1000 + 2000r + 1000r2 = 1123.60

Solving for variable 'r'.

Reorder the terms:
1000 + -1123.60 + 2000r + 1000r2 = 1123.60 + -1123.60

Combine like terms: 1000 + -1123.60 = -123.6
-123.6 + 2000r + 1000r2 = 1123.60 + -1123.60

Combine like terms: 1123.60 + -1123.60 = 0.00
-123.6 + 2000r + 1000r2 = 0.00

Begin completing the square.  Divide all terms by
1000 the coefficient of the squared term: 

Divide each side by '1000'.
-0.1236 + 2r + r2 = 0.00

Move the constant term to the right:

Add '0.1236' to each side of the equation.
-0.1236 + 2r + 0.1236 + r2 = 0.00 + 0.1236

Reorder the terms:
-0.1236 + 0.1236 + 2r + r2 = 0.00 + 0.1236

Combine like terms: -0.1236 + 0.1236 = 0.0000
0.0000 + 2r + r2 = 0.00 + 0.1236
2r + r2 = 0.00 + 0.1236

Combine like terms: 0.00 + 0.1236 = 0.1236
2r + r2 = 0.1236

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 = 0.1236 + 1

Reorder the terms:
1 + 2r + r2 = 0.1236 + 1

Combine like terms: 0.1236 + 1 = 1.1236
1 + 2r + r2 = 1.1236

Factor a perfect square on the left side:
(r + 1)(r + 1) = 1.1236

Calculate the square root of the right side: 1.06

Break this problem into two subproblems by setting 
(r + 1) equal to 1.06 and -1.06.

Subproblem 1
r + 1 = 1.06

Simplifying
r + 1 = 1.06

Reorder the terms:
1 + r = 1.06

Solving
1 + r = 1.06

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 = 1.06 + -1

Combine like terms: 1 + -1 = 0
0 + r = 1.06 + -1
r = 1.06 + -1

Combine like terms: 1.06 + -1 = 0.06
r = 0.06

Simplifying
r = 0.06

Subproblem 2
r + 1 = -1.06

Simplifying
r + 1 = -1.06

Reorder the terms:
1 + r = -1.06

Solving
1 + r = -1.06

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 = -1.06 + -1

Combine like terms: 1 + -1 = 0
0 + r = -1.06 + -1
r = -1.06 + -1

Combine like terms: -1.06 + -1 = -2.06
r = -2.06

Simplifying
r = -2.06

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.06, -2.06}