(x+1)(x+1)=2.25

Solution for (x+1)(x+1)=2.25 equation:

Simplifying
(x + 1)(x + 1) = 2.25

Reorder the terms:
(1 + x)(x + 1) = 2.25

Reorder the terms:
(1 + x)(1 + x) = 2.25

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) = 2.25
((1 * 1 + x * 1) + x(1 + x)) = 2.25
((1 + 1x) + x(1 + x)) = 2.25
(1 + 1x + (1 * x + x * x)) = 2.25
(1 + 1x + (1x + x2)) = 2.25

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) = 2.25

Solving
1 + 2x + x2 = 2.25

Solving for variable 'x'.

Reorder the terms:
1 + -2.25 + 2x + x2 = 2.25 + -2.25

Combine like terms: 1 + -2.25 = -1.25
-1.25 + 2x + x2 = 2.25 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
-1.25 + 2x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2x + 1.25 + x2 = 0.00 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2x + x2 = 0.00 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2x + x2 = 0.00 + 1.25
2x + x2 = 0.00 + 1.25

Combine like terms: 0.00 + 1.25 = 1.25
2x + x2 = 1.25

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 = 1.25 + 1

Reorder the terms:
1 + 2x + x2 = 1.25 + 1

Combine like terms: 1.25 + 1 = 2.25
1 + 2x + x2 = 2.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x + 1) equal to 1.5 and -1.5.

Subproblem 1
x + 1 = 1.5

Simplifying
x + 1 = 1.5

Reorder the terms:
1 + x = 1.5

Solving
1 + x = 1.5

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 = 1.5 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.5 + -1
x = 1.5 + -1

Combine like terms: 1.5 + -1 = 0.5
x = 0.5

Simplifying
x = 0.5

Subproblem 2
x + 1 = -1.5

Simplifying
x + 1 = -1.5

Reorder the terms:
1 + x = -1.5

Solving
1 + x = -1.5

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 = -1.5 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.5 + -1
x = -1.5 + -1

Combine like terms: -1.5 + -1 = -2.5
x = -2.5

Simplifying
x = -2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -2.5}