x^2+3x+2.25=0

Solution for x^2+3x+2.25=0 equation:

Simplifying
x2 + 3x + 2.25 = 0

Reorder the terms:
2.25 + 3x + x2 = 0

Solving
2.25 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + 3x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 3x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 3x + x2 = 0 + -2.25
3x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
3x + x2 = -2.25

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -2.25 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -2.25 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
2.25 + 3x + x2 = 0.00

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + 1.5) equal to 0.00 and 0.00.

Subproblem 1
x + 1.5 = 0.00

Simplifying
x + 1.5 = 0.00

Reorder the terms:
1.5 + x = 0.00

Solving
1.5 + x = 0.00

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 0.00 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 0.00 + -1.5
x = 0.00 + -1.5

Combine like terms: 0.00 + -1.5 = -1.5
x = -1.5

Simplifying
x = -1.5

Subproblem 2
x + 1.5 = 0.00

Simplifying
x + 1.5 = 0.00

Reorder the terms:
1.5 + x = 0.00

Solving
1.5 + x = 0.00

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 0.00 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 0.00 + -1.5
x = 0.00 + -1.5

Combine like terms: 0.00 + -1.5 = -1.5
x = -1.5

Simplifying
x = -1.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.5, -1.5}