y(70-1y)-y=11

Solution for y(70-1y)-y=11 equation:

Simplifying
y(70 + -1y) + -1y = 11
(70 * y + -1y * y) + -1y = 11
(70y + -1y2) + -1y = 11

Reorder the terms:
70y + -1y + -1y2 = 11

Combine like terms: 70y + -1y = 69y
69y + -1y2 = 11

Solving
69y + -1y2 = 11

Solving for variable 'y'.

Reorder the terms:
-11 + 69y + -1y2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 69y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
11 + -69y + y2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -69y + -11 + y2 = 0 + -11

Reorder the terms:
11 + -11 + -69y + y2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -69y + y2 = 0 + -11
-69y + y2 = 0 + -11

Combine like terms: 0 + -11 = -11
-69y + y2 = -11

The y term is -69y.  Take half its coefficient (-34.5).
Square it (1190.25) and add it to both sides.

Add '1190.25' to each side of the equation.
-69y + 1190.25 + y2 = -11 + 1190.25

Reorder the terms:
1190.25 + -69y + y2 = -11 + 1190.25

Combine like terms: -11 + 1190.25 = 1179.25
1190.25 + -69y + y2 = 1179.25

Factor a perfect square on the left side:
(y + -34.5)(y + -34.5) = 1179.25

Calculate the square root of the right side: 34.340209667

Break this problem into two subproblems by setting 
(y + -34.5) equal to 34.340209667 and -34.340209667.

Subproblem 1
y + -34.5 = 34.340209667

Simplifying
y + -34.5 = 34.340209667

Reorder the terms:
-34.5 + y = 34.340209667

Solving
-34.5 + y = 34.340209667

Solving for variable 'y'.

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

Add '34.5' to each side of the equation.
-34.5 + 34.5 + y = 34.340209667 + 34.5

Combine like terms: -34.5 + 34.5 = 0.0
0.0 + y = 34.340209667 + 34.5
y = 34.340209667 + 34.5

Combine like terms: 34.340209667 + 34.5 = 68.840209667
y = 68.840209667

Simplifying
y = 68.840209667

Subproblem 2
y + -34.5 = -34.340209667

Simplifying
y + -34.5 = -34.340209667

Reorder the terms:
-34.5 + y = -34.340209667

Solving
-34.5 + y = -34.340209667

Solving for variable 'y'.

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

Add '34.5' to each side of the equation.
-34.5 + 34.5 + y = -34.340209667 + 34.5

Combine like terms: -34.5 + 34.5 = 0.0
0.0 + y = -34.340209667 + 34.5
y = -34.340209667 + 34.5

Combine like terms: -34.340209667 + 34.5 = 0.159790333
y = 0.159790333

Simplifying
y = 0.159790333

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {68.840209667, 0.159790333}