2000(1+x)(1+x)=2200

Solution for 2000(1+x)(1+x)=2200 equation:

Simplifying
2000(1 + x)(1 + x) = 2200

Multiply (1 + x) * (1 + x)
2000(1(1 + x) + x(1 + x)) = 2200
2000((1 * 1 + x * 1) + x(1 + x)) = 2200
2000((1 + 1x) + x(1 + x)) = 2200
2000(1 + 1x + (1 * x + x * x)) = 2200
2000(1 + 1x + (1x + x2)) = 2200

Combine like terms: 1x + 1x = 2x
2000(1 + 2x + x2) = 2200
(1 * 2000 + 2x * 2000 + x2 * 2000) = 2200
(2000 + 4000x + 2000x2) = 2200

Solving
2000 + 4000x + 2000x2 = 2200

Solving for variable 'x'.

Reorder the terms:
2000 + -2200 + 4000x + 2000x2 = 2200 + -2200

Combine like terms: 2000 + -2200 = -200
-200 + 4000x + 2000x2 = 2200 + -2200

Combine like terms: 2200 + -2200 = 0
-200 + 4000x + 2000x2 = 0

Factor out the Greatest Common Factor (GCF), '200'.
200(-1 + 20x + 10x2) = 0

Ignore the factor 200.
Subproblem 1
Set the factor '(-1 + 20x + 10x2)' equal to zero and attempt to solve:

Simplifying
-1 + 20x + 10x2 = 0

Solving
-1 + 20x + 10x2 = 0

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

Divide each side by '10'.
-0.1 + 2x + x2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 2x + 0.1 + x2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 2x + x2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 2x + x2 = 0.0 + 0.1
2x + x2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
2x + x2 = 0.1

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

Add '1' to each side of the equation.
2x + 1 + x2 = 0.1 + 1

Reorder the terms:
1 + 2x + x2 = 0.1 + 1

Combine like terms: 0.1 + 1 = 1.1
1 + 2x + x2 = 1.1

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.1

Calculate the square root of the right side: 1.048808848

Break this problem into two subproblems by setting 
(x + 1) equal to 1.048808848 and -1.048808848.

Subproblem 1
x + 1 = 1.048808848

Simplifying
x + 1 = 1.048808848

Reorder the terms:
1 + x = 1.048808848

Solving
1 + x = 1.048808848

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.048808848 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.048808848 + -1
x = 1.048808848 + -1

Combine like terms: 1.048808848 + -1 = 0.048808848
x = 0.048808848

Simplifying
x = 0.048808848

Subproblem 2
x + 1 = -1.048808848

Simplifying
x + 1 = -1.048808848

Reorder the terms:
1 + x = -1.048808848

Solving
1 + x = -1.048808848

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.048808848 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.048808848 + -1
x = -1.048808848 + -1

Combine like terms: -1.048808848 + -1 = -2.048808848
x = -2.048808848

Simplifying
x = -2.048808848

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.048808848, -2.048808848}
Solution
x = {0.048808848, -2.048808848}