y^2+11y-45=0

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


Simplifying
y2 + 11y + -45 = 0

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

Solving
-45 + 11y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 11y + 45 + y2 = 0 + 45

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

Combine like terms: -45 + 45 = 0
0 + 11y + y2 = 0 + 45
11y + y2 = 0 + 45

Combine like terms: 0 + 45 = 45
11y + y2 = 45

The y term is 11y.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11y + 30.25 + y2 = 45 + 30.25

Reorder the terms:
30.25 + 11y + y2 = 45 + 30.25

Combine like terms: 45 + 30.25 = 75.25
30.25 + 11y + y2 = 75.25

Factor a perfect square on the left side:
(y + 5.5)(y + 5.5) = 75.25

Calculate the square root of the right side: 8.674675786

Break this problem into two subproblems by setting 
(y + 5.5) equal to 8.674675786 and -8.674675786.


Subproblem 1
y + 5.5 = 8.674675786

Simplifying
y + 5.5 = 8.674675786

Reorder the terms:
5.5 + y = 8.674675786

Solving
5.5 + y = 8.674675786

Solving for variable 'y'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + y = 8.674675786 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + y = 8.674675786 + -5.5
y = 8.674675786 + -5.5

Combine like terms: 8.674675786 + -5.5 = 3.174675786
y = 3.174675786

Simplifying
y = 3.174675786


Subproblem 2
y + 5.5 = -8.674675786

Simplifying
y + 5.5 = -8.674675786

Reorder the terms:
5.5 + y = -8.674675786

Solving
5.5 + y = -8.674675786

Solving for variable 'y'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + y = -8.674675786 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + y = -8.674675786 + -5.5
y = -8.674675786 + -5.5

Combine like terms: -8.674675786 + -5.5 = -14.174675786
y = -14.174675786

Simplifying
y = -14.174675786


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.174675786, -14.174675786}

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