(66+y)*(55+y)=33

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Solution for (66+y)*(55+y)=33 equation: 


Simplifying
(66 + y)(55 + y) = 33

Multiply (66 + y) * (55 + y)
(66(55 + y) + y(55 + y)) = 33
((55 * 66 + y * 66) + y(55 + y)) = 33
((3630 + 66y) + y(55 + y)) = 33
(3630 + 66y + (55 * y + y * y)) = 33
(3630 + 66y + (55y + y2)) = 33

Combine like terms: 66y + 55y = 121y
(3630 + 121y + y2) = 33

Solving
3630 + 121y + y2 = 33

Solving for variable 'y'.

Reorder the terms:
3630 + -33 + 121y + y2 = 33 + -33

Combine like terms: 3630 + -33 = 3597
3597 + 121y + y2 = 33 + -33

Combine like terms: 33 + -33 = 0
3597 + 121y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3597' to each side of the equation.
3597 + 121y + -3597 + y2 = 0 + -3597

Reorder the terms:
3597 + -3597 + 121y + y2 = 0 + -3597

Combine like terms: 3597 + -3597 = 0
0 + 121y + y2 = 0 + -3597
121y + y2 = 0 + -3597

Combine like terms: 0 + -3597 = -3597
121y + y2 = -3597

The y term is 121y.  Take half its coefficient (60.5).
Square it (3660.25) and add it to both sides.

Add '3660.25' to each side of the equation.
121y + 3660.25 + y2 = -3597 + 3660.25

Reorder the terms:
3660.25 + 121y + y2 = -3597 + 3660.25

Combine like terms: -3597 + 3660.25 = 63.25
3660.25 + 121y + y2 = 63.25

Factor a perfect square on the left side:
(y + 60.5)(y + 60.5) = 63.25

Calculate the square root of the right side: 7.95298686

Break this problem into two subproblems by setting 
(y + 60.5) equal to 7.95298686 and -7.95298686.


Subproblem 1
y + 60.5 = 7.95298686

Simplifying
y + 60.5 = 7.95298686

Reorder the terms:
60.5 + y = 7.95298686

Solving
60.5 + y = 7.95298686

Solving for variable 'y'.

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

Add '-60.5' to each side of the equation.
60.5 + -60.5 + y = 7.95298686 + -60.5

Combine like terms: 60.5 + -60.5 = 0.0
0.0 + y = 7.95298686 + -60.5
y = 7.95298686 + -60.5

Combine like terms: 7.95298686 + -60.5 = -52.54701314
y = -52.54701314

Simplifying
y = -52.54701314


Subproblem 2
y + 60.5 = -7.95298686

Simplifying
y + 60.5 = -7.95298686

Reorder the terms:
60.5 + y = -7.95298686

Solving
60.5 + y = -7.95298686

Solving for variable 'y'.

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

Add '-60.5' to each side of the equation.
60.5 + -60.5 + y = -7.95298686 + -60.5

Combine like terms: 60.5 + -60.5 = 0.0
0.0 + y = -7.95298686 + -60.5
y = -7.95298686 + -60.5

Combine like terms: -7.95298686 + -60.5 = -68.45298686
y = -68.45298686

Simplifying
y = -68.45298686


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-52.54701314, -68.45298686}

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