(x+1)(x-2)=-2.25

Solution for (x+1)(x-2)=-2.25 equation:

Simplifying
(x + 1)(x + -2) = -2.25

Reorder the terms:
(1 + x)(x + -2) = -2.25

Reorder the terms:
(1 + x)(-2 + x) = -2.25

Multiply (1 + x) * (-2 + x)
(1(-2 + x) + x(-2 + x)) = -2.25
((-2 * 1 + x * 1) + x(-2 + x)) = -2.25
((-2 + 1x) + x(-2 + x)) = -2.25
(-2 + 1x + (-2 * x + x * x)) = -2.25
(-2 + 1x + (-2x + x2)) = -2.25

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

Solving
-2 + -1x + x2 = -2.25

Solving for variable 'x'.

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

Combine like terms: -2 + 2.25 = 0.25
0.25 + -1x + x2 = -2.25 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.25 + -1x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1x + -0.25 + x2 = 0.00 + -0.25

Reorder the terms:
0.25 + -0.25 + -1x + x2 = 0.00 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1x + x2 = 0.00 + -0.25
-1x + x2 = 0.00 + -0.25

Combine like terms: 0.00 + -0.25 = -0.25
-1x + x2 = -0.25

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.25 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -1x + x2 = 0.00

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.00 and 0.00.

Subproblem 1
x + -0.5 = 0.00

Simplifying
x + -0.5 = 0.00

Reorder the terms:
-0.5 + x = 0.00

Solving
-0.5 + x = 0.00

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.00 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.00 + 0.5
x = 0.00 + 0.5

Combine like terms: 0.00 + 0.5 = 0.5
x = 0.5

Simplifying
x = 0.5

Subproblem 2
x + -0.5 = 0.00

Simplifying
x + -0.5 = 0.00

Reorder the terms:
-0.5 + x = 0.00

Solving
-0.5 + x = 0.00

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.00 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.00 + 0.5
x = 0.00 + 0.5

Combine like terms: 0.00 + 0.5 = 0.5
x = 0.5

Simplifying
x = 0.5

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