11y^2-45y-36=0

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Solution for 11y^2-45y-36=0 equation: 


Simplifying
11y2 + -45y + -36 = 0

Reorder the terms:
-36 + -45y + 11y2 = 0

Solving
-36 + -45y + 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'.
-3.272727273 + -4.090909091y + y2 = 0

Move the constant term to the right:

Add '3.272727273' to each side of the equation.
-3.272727273 + -4.090909091y + 3.272727273 + y2 = 0 + 3.272727273

Reorder the terms:
-3.272727273 + 3.272727273 + -4.090909091y + y2 = 0 + 3.272727273

Combine like terms: -3.272727273 + 3.272727273 = 0.000000000
0.000000000 + -4.090909091y + y2 = 0 + 3.272727273
-4.090909091y + y2 = 0 + 3.272727273

Combine like terms: 0 + 3.272727273 = 3.272727273
-4.090909091y + y2 = 3.272727273

The y term is -4.090909091y.  Take half its coefficient (-2.045454546).
Square it (4.183884300) and add it to both sides.

Add '4.183884300' to each side of the equation.
-4.090909091y + 4.183884300 + y2 = 3.272727273 + 4.183884300

Reorder the terms:
4.183884300 + -4.090909091y + y2 = 3.272727273 + 4.183884300

Combine like terms: 3.272727273 + 4.183884300 = 7.456611573
4.183884300 + -4.090909091y + y2 = 7.456611573

Factor a perfect square on the left side:
(y + -2.045454546)(y + -2.045454546) = 7.456611573

Calculate the square root of the right side: 2.730679691

Break this problem into two subproblems by setting 
(y + -2.045454546) equal to 2.730679691 and -2.730679691.


Subproblem 1
y + -2.045454546 = 2.730679691

Simplifying
y + -2.045454546 = 2.730679691

Reorder the terms:
-2.045454546 + y = 2.730679691

Solving
-2.045454546 + y = 2.730679691

Solving for variable 'y'.

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

Add '2.045454546' to each side of the equation.
-2.045454546 + 2.045454546 + y = 2.730679691 + 2.045454546

Combine like terms: -2.045454546 + 2.045454546 = 0.000000000
0.000000000 + y = 2.730679691 + 2.045454546
y = 2.730679691 + 2.045454546

Combine like terms: 2.730679691 + 2.045454546 = 4.776134237
y = 4.776134237

Simplifying
y = 4.776134237


Subproblem 2
y + -2.045454546 = -2.730679691

Simplifying
y + -2.045454546 = -2.730679691

Reorder the terms:
-2.045454546 + y = -2.730679691

Solving
-2.045454546 + y = -2.730679691

Solving for variable 'y'.

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

Add '2.045454546' to each side of the equation.
-2.045454546 + 2.045454546 + y = -2.730679691 + 2.045454546

Combine like terms: -2.045454546 + 2.045454546 = 0.000000000
0.000000000 + y = -2.730679691 + 2.045454546
y = -2.730679691 + 2.045454546

Combine like terms: -2.730679691 + 2.045454546 = -0.685225145
y = -0.685225145

Simplifying
y = -0.685225145


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.776134237, -0.685225145}

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