y^2-11y+15=0

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Solution for y^2-11y+15=0 equation: 


Simplifying
y2 + -11y + 15 = 0

Reorder the terms:
15 + -11y + y2 = 0

Solving
15 + -11y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -11y + -15 + y2 = 0 + -15

Reorder the terms:
15 + -15 + -11y + y2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -11y + y2 = 0 + -15
-11y + y2 = 0 + -15

Combine like terms: 0 + -15 = -15
-11y + y2 = -15

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 = -15 + 30.25

Reorder the terms:
30.25 + -11y + y2 = -15 + 30.25

Combine like terms: -15 + 30.25 = 15.25
30.25 + -11y + y2 = 15.25

Factor a perfect square on the left side:
(y + -5.5)(y + -5.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(y + -5.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
y + -5.5 = 3.905124838

Simplifying
y + -5.5 = 3.905124838

Reorder the terms:
-5.5 + y = 3.905124838

Solving
-5.5 + y = 3.905124838

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 = 3.905124838 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = 3.905124838 + 5.5
y = 3.905124838 + 5.5

Combine like terms: 3.905124838 + 5.5 = 9.405124838
y = 9.405124838

Simplifying
y = 9.405124838


Subproblem 2
y + -5.5 = -3.905124838

Simplifying
y + -5.5 = -3.905124838

Reorder the terms:
-5.5 + y = -3.905124838

Solving
-5.5 + y = -3.905124838

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 = -3.905124838 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = -3.905124838 + 5.5
y = -3.905124838 + 5.5

Combine like terms: -3.905124838 + 5.5 = 1.594875162
y = 1.594875162

Simplifying
y = 1.594875162


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.405124838, 1.594875162}

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