-1.1+0.4y^2=-0.9y

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Solution for -1.1+0.4y^2=-0.9y equation: 


Simplifying
-1.1 + 0.4y2 = -0.9y

Solving
-1.1 + 0.4y2 = -0.9y

Solving for variable 'y'.

Reorder the terms:
-1.1 + 0.9y + 0.4y2 = -0.9y + 0.9y

Combine like terms: -0.9y + 0.9y = 0.0
-1.1 + 0.9y + 0.4y2 = 0.0

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

Divide each side by '0.4'.
-2.75 + 2.25y + y2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 2.25y + 2.75 + y2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 2.25y + y2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 2.25y + y2 = 0 + 2.75
2.25y + y2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
2.25y + y2 = 2.75

The y term is 2.25y.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25y + 1.265625 + y2 = 2.75 + 1.265625

Reorder the terms:
1.265625 + 2.25y + y2 = 2.75 + 1.265625

Combine like terms: 2.75 + 1.265625 = 4.015625
1.265625 + 2.25y + y2 = 4.015625

Factor a perfect square on the left side:
(y + 1.125)(y + 1.125) = 4.015625

Calculate the square root of the right side: 2.003902443

Break this problem into two subproblems by setting 
(y + 1.125) equal to 2.003902443 and -2.003902443.


Subproblem 1
y + 1.125 = 2.003902443

Simplifying
y + 1.125 = 2.003902443

Reorder the terms:
1.125 + y = 2.003902443

Solving
1.125 + y = 2.003902443

Solving for variable 'y'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + y = 2.003902443 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + y = 2.003902443 + -1.125
y = 2.003902443 + -1.125

Combine like terms: 2.003902443 + -1.125 = 0.878902443
y = 0.878902443

Simplifying
y = 0.878902443


Subproblem 2
y + 1.125 = -2.003902443

Simplifying
y + 1.125 = -2.003902443

Reorder the terms:
1.125 + y = -2.003902443

Solving
1.125 + y = -2.003902443

Solving for variable 'y'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + y = -2.003902443 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + y = -2.003902443 + -1.125
y = -2.003902443 + -1.125

Combine like terms: -2.003902443 + -1.125 = -3.128902443
y = -3.128902443

Simplifying
y = -3.128902443


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.878902443, -3.128902443}

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