y=2.25(16y+3.25)y+1

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Solution for y=2.25(16y+3.25)y+1 equation: 


Simplifying
y = 2.25(16y + 3.25) * y + 1

Reorder the terms:
y = 2.25(3.25 + 16y) * y + 1

Reorder the terms for easier multiplication:
y = 2.25y(3.25 + 16y) + 1
y = (3.25 * 2.25y + 16y * 2.25y) + 1
y = (7.3125y + 36y2) + 1

Reorder the terms:
y = 1 + 7.3125y + 36y2

Solving
y = 1 + 7.3125y + 36y2

Solving for variable 'y'.

Reorder the terms:
-1 + y + -7.3125y + -36y2 = 1 + 7.3125y + 36y2 + -1 + -7.3125y + -36y2

Combine like terms: y + -7.3125y = -6.3125y
-1 + -6.3125y + -36y2 = 1 + 7.3125y + 36y2 + -1 + -7.3125y + -36y2

Reorder the terms:
-1 + -6.3125y + -36y2 = 1 + -1 + 7.3125y + -7.3125y + 36y2 + -36y2

Combine like terms: 1 + -1 = 0
-1 + -6.3125y + -36y2 = 0 + 7.3125y + -7.3125y + 36y2 + -36y2
-1 + -6.3125y + -36y2 = 7.3125y + -7.3125y + 36y2 + -36y2

Combine like terms: 7.3125y + -7.3125y = 0.0000
-1 + -6.3125y + -36y2 = 0.0000 + 36y2 + -36y2
-1 + -6.3125y + -36y2 = 36y2 + -36y2

Combine like terms: 36y2 + -36y2 = 0
-1 + -6.3125y + -36y2 = 0

Begin completing the square.  Divide all terms by
-36 the coefficient of the squared term: 

Divide each side by '-36'.
0.02777777778 + 0.1753472222y + y2 = 0

Move the constant term to the right:

Add '-0.02777777778' to each side of the equation.
0.02777777778 + 0.1753472222y + -0.02777777778 + y2 = 0 + -0.02777777778

Reorder the terms:
0.02777777778 + -0.02777777778 + 0.1753472222y + y2 = 0 + -0.02777777778

Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000
0.00000000000 + 0.1753472222y + y2 = 0 + -0.02777777778
0.1753472222y + y2 = 0 + -0.02777777778

Combine like terms: 0 + -0.02777777778 = -0.02777777778
0.1753472222y + y2 = -0.02777777778

The y term is 0.1753472222y.  Take half its coefficient (0.0876736111).
Square it (0.007686662083) and add it to both sides.

Add '0.007686662083' to each side of the equation.
0.1753472222y + 0.007686662083 + y2 = -0.02777777778 + 0.007686662083

Reorder the terms:
0.007686662083 + 0.1753472222y + y2 = -0.02777777778 + 0.007686662083

Combine like terms: -0.02777777778 + 0.007686662083 = -0.020091115697
0.007686662083 + 0.1753472222y + y2 = -0.020091115697

Factor a perfect square on the left side:
(y + 0.0876736111)(y + 0.0876736111) = -0.020091115697

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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