11y^2-72y+13=0

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Solution for 11y^2-72y+13=0 equation: 


Simplifying
11y2 + -72y + 13 = 0

Reorder the terms:
13 + -72y + 11y2 = 0

Solving
13 + -72y + 11y2 = 0

Solving for variable 'y'.

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

Divide each side by '11'.
1.181818182 + -6.545454545y + y2 = 0

Move the constant term to the right:

Add '-1.181818182' to each side of the equation.
1.181818182 + -6.545454545y + -1.181818182 + y2 = 0 + -1.181818182

Reorder the terms:
1.181818182 + -1.181818182 + -6.545454545y + y2 = 0 + -1.181818182

Combine like terms: 1.181818182 + -1.181818182 = 0.000000000
0.000000000 + -6.545454545y + y2 = 0 + -1.181818182
-6.545454545y + y2 = 0 + -1.181818182

Combine like terms: 0 + -1.181818182 = -1.181818182
-6.545454545y + y2 = -1.181818182

The y term is -6.545454545y.  Take half its coefficient (-3.272727273).
Square it (10.71074380) and add it to both sides.

Add '10.71074380' to each side of the equation.
-6.545454545y + 10.71074380 + y2 = -1.181818182 + 10.71074380

Reorder the terms:
10.71074380 + -6.545454545y + y2 = -1.181818182 + 10.71074380

Combine like terms: -1.181818182 + 10.71074380 = 9.528925618
10.71074380 + -6.545454545y + y2 = 9.528925618

Factor a perfect square on the left side:
(y + -3.272727273)(y + -3.272727273) = 9.528925618

Calculate the square root of the right side: 3.08689579

Break this problem into two subproblems by setting 
(y + -3.272727273) equal to 3.08689579 and -3.08689579.


Subproblem 1
y + -3.272727273 = 3.08689579

Simplifying
y + -3.272727273 = 3.08689579

Reorder the terms:
-3.272727273 + y = 3.08689579

Solving
-3.272727273 + y = 3.08689579

Solving for variable 'y'.

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

Add '3.272727273' to each side of the equation.
-3.272727273 + 3.272727273 + y = 3.08689579 + 3.272727273

Combine like terms: -3.272727273 + 3.272727273 = 0.000000000
0.000000000 + y = 3.08689579 + 3.272727273
y = 3.08689579 + 3.272727273

Combine like terms: 3.08689579 + 3.272727273 = 6.359623063
y = 6.359623063

Simplifying
y = 6.359623063


Subproblem 2
y + -3.272727273 = -3.08689579

Simplifying
y + -3.272727273 = -3.08689579

Reorder the terms:
-3.272727273 + y = -3.08689579

Solving
-3.272727273 + y = -3.08689579

Solving for variable 'y'.

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

Add '3.272727273' to each side of the equation.
-3.272727273 + 3.272727273 + y = -3.08689579 + 3.272727273

Combine like terms: -3.272727273 + 3.272727273 = 0.000000000
0.000000000 + y = -3.08689579 + 3.272727273
y = -3.08689579 + 3.272727273

Combine like terms: -3.08689579 + 3.272727273 = 0.185831483
y = 0.185831483

Simplifying
y = 0.185831483


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.359623063, 0.185831483}

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