y^2+3y+2.25=.75

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Solution for y^2+3y+2.25=.75 equation: 


Simplifying
y2 + 3y + 2.25 = 0.75

Reorder the terms:
2.25 + 3y + y2 = 0.75

Solving
2.25 + 3y + y2 = 0.75

Solving for variable 'y'.

Reorder the terms:
2.25 + -0.75 + 3y + y2 = 0.75 + -0.75

Combine like terms: 2.25 + -0.75 = 1.5
1.5 + 3y + y2 = 0.75 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
1.5 + 3y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 3y + -1.5 + y2 = 0.00 + -1.5

Reorder the terms:
1.5 + -1.5 + 3y + y2 = 0.00 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 3y + y2 = 0.00 + -1.5
3y + y2 = 0.00 + -1.5

Combine like terms: 0.00 + -1.5 = -1.5
3y + y2 = -1.5

The y term is 3y.  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.
3y + 2.25 + y2 = -1.5 + 2.25

Reorder the terms:
2.25 + 3y + y2 = -1.5 + 2.25

Combine like terms: -1.5 + 2.25 = 0.75
2.25 + 3y + y2 = 0.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(y + 1.5) equal to 0.866025404 and -0.866025404.


Subproblem 1
y + 1.5 = 0.866025404

Simplifying
y + 1.5 = 0.866025404

Reorder the terms:
1.5 + y = 0.866025404

Solving
1.5 + y = 0.866025404

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 0.866025404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 0.866025404 + -1.5
y = 0.866025404 + -1.5

Combine like terms: 0.866025404 + -1.5 = -0.633974596
y = -0.633974596

Simplifying
y = -0.633974596


Subproblem 2
y + 1.5 = -0.866025404

Simplifying
y + 1.5 = -0.866025404

Reorder the terms:
1.5 + y = -0.866025404

Solving
1.5 + y = -0.866025404

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -0.866025404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -0.866025404 + -1.5
y = -0.866025404 + -1.5

Combine like terms: -0.866025404 + -1.5 = -2.366025404
y = -2.366025404

Simplifying
y = -2.366025404


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.633974596, -2.366025404}

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