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Simplifying
3y2 + -2.55y + -1.0 = 0.5

Reorder the terms:
-1.0 + -2.55y + 3y2 = 0.5

Solving
-1.0 + -2.55y + 3y2 = 0.5

Solving for variable 'y'.

Reorder the terms:
-1.0 + -0.5 + -2.55y + 3y2 = 0.5 + -0.5

Combine like terms: -1.0 + -0.5 = -1.5
-1.5 + -2.55y + 3y2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-1.5 + -2.55y + 3y2 = 0.0

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

Divide each side by '3'.
-0.5 + -0.85y + y2 = 0.0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.85y + 0.5 + y2 = 0.0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.85y + y2 = 0.0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.85y + y2 = 0.0 + 0.5
-0.85y + y2 = 0.0 + 0.5

Combine like terms: 0.0 + 0.5 = 0.5
-0.85y + y2 = 0.5

The y term is -0.85y.  Take half its coefficient (-0.425).
Square it (0.180625) and add it to both sides.

Add '0.180625' to each side of the equation.
-0.85y + 0.180625 + y2 = 0.5 + 0.180625

Reorder the terms:
0.180625 + -0.85y + y2 = 0.5 + 0.180625

Combine like terms: 0.5 + 0.180625 = 0.680625
0.180625 + -0.85y + y2 = 0.680625

Factor a perfect square on the left side:
(y + -0.425)(y + -0.425) = 0.680625

Calculate the square root of the right side: 0.825

Break this problem into two subproblems by setting 
(y + -0.425) equal to 0.825 and -0.825.

Subproblem 1

y + -0.425 = 0.825 Simplifying y + -0.425 = 0.825 Reorder the terms: -0.425 + y = 0.825 Solving -0.425 + y = 0.825 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.425' to each side of the equation. -0.425 + 0.425 + y = 0.825 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + y = 0.825 + 0.425 y = 0.825 + 0.425 Combine like terms: 0.825 + 0.425 = 1.25 y = 1.25 Simplifying y = 1.25

Subproblem 2

y + -0.425 = -0.825 Simplifying y + -0.425 = -0.825 Reorder the terms: -0.425 + y = -0.825 Solving -0.425 + y = -0.825 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.425' to each side of the equation. -0.425 + 0.425 + y = -0.825 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + y = -0.825 + 0.425 y = -0.825 + 0.425 Combine like terms: -0.825 + 0.425 = -0.4 y = -0.4 Simplifying y = -0.4

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.25, -0.4}
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