0.44y^2+2y-4=0

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Solution for 0.44y^2+2y-4=0 equation: 


Simplifying
0.44y2 + 2y + -4 = 0

Reorder the terms:
-4 + 2y + 0.44y2 = 0

Solving
-4 + 2y + 0.44y2 = 0

Solving for variable 'y'.

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

Divide each side by '0.44'.
-9.090909091 + 4.545454545y + y2 = 0

Move the constant term to the right:

Add '9.090909091' to each side of the equation.
-9.090909091 + 4.545454545y + 9.090909091 + y2 = 0 + 9.090909091

Reorder the terms:
-9.090909091 + 9.090909091 + 4.545454545y + y2 = 0 + 9.090909091

Combine like terms: -9.090909091 + 9.090909091 = 0.000000000
0.000000000 + 4.545454545y + y2 = 0 + 9.090909091
4.545454545y + y2 = 0 + 9.090909091

Combine like terms: 0 + 9.090909091 = 9.090909091
4.545454545y + y2 = 9.090909091

The y term is 4.545454545y.  Take half its coefficient (2.272727273).
Square it (5.165289257) and add it to both sides.

Add '5.165289257' to each side of the equation.
4.545454545y + 5.165289257 + y2 = 9.090909091 + 5.165289257

Reorder the terms:
5.165289257 + 4.545454545y + y2 = 9.090909091 + 5.165289257

Combine like terms: 9.090909091 + 5.165289257 = 14.256198348
5.165289257 + 4.545454545y + y2 = 14.256198348

Factor a perfect square on the left side:
(y + 2.272727273)(y + 2.272727273) = 14.256198348

Calculate the square root of the right side: 3.77573812

Break this problem into two subproblems by setting 
(y + 2.272727273) equal to 3.77573812 and -3.77573812.


Subproblem 1
y + 2.272727273 = 3.77573812

Simplifying
y + 2.272727273 = 3.77573812

Reorder the terms:
2.272727273 + y = 3.77573812

Solving
2.272727273 + y = 3.77573812

Solving for variable 'y'.

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

Add '-2.272727273' to each side of the equation.
2.272727273 + -2.272727273 + y = 3.77573812 + -2.272727273

Combine like terms: 2.272727273 + -2.272727273 = 0.000000000
0.000000000 + y = 3.77573812 + -2.272727273
y = 3.77573812 + -2.272727273

Combine like terms: 3.77573812 + -2.272727273 = 1.503010847
y = 1.503010847

Simplifying
y = 1.503010847


Subproblem 2
y + 2.272727273 = -3.77573812

Simplifying
y + 2.272727273 = -3.77573812

Reorder the terms:
2.272727273 + y = -3.77573812

Solving
2.272727273 + y = -3.77573812

Solving for variable 'y'.

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

Add '-2.272727273' to each side of the equation.
2.272727273 + -2.272727273 + y = -3.77573812 + -2.272727273

Combine like terms: 2.272727273 + -2.272727273 = 0.000000000
0.000000000 + y = -3.77573812 + -2.272727273
y = -3.77573812 + -2.272727273

Combine like terms: -3.77573812 + -2.272727273 = -6.048465393
y = -6.048465393

Simplifying
y = -6.048465393


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.503010847, -6.048465393}

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