y^2-11y+21=0

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Solution for y^2-11y+21=0 equation: 


Simplifying
y2 + -11y + 21 = 0

Reorder the terms:
21 + -11y + y2 = 0

Solving
21 + -11y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -11y + -21 + y2 = 0 + -21

Reorder the terms:
21 + -21 + -11y + y2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -11y + y2 = 0 + -21
-11y + y2 = 0 + -21

Combine like terms: 0 + -21 = -21
-11y + y2 = -21

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 = -21 + 30.25

Reorder the terms:
30.25 + -11y + y2 = -21 + 30.25

Combine like terms: -21 + 30.25 = 9.25
30.25 + -11y + y2 = 9.25

Factor a perfect square on the left side:
(y + -5.5)(y + -5.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(y + -5.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
y + -5.5 = 3.041381265

Simplifying
y + -5.5 = 3.041381265

Reorder the terms:
-5.5 + y = 3.041381265

Solving
-5.5 + y = 3.041381265

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 = 3.041381265 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = 3.041381265 + 5.5
y = 3.041381265 + 5.5

Combine like terms: 3.041381265 + 5.5 = 8.541381265
y = 8.541381265

Simplifying
y = 8.541381265


Subproblem 2
y + -5.5 = -3.041381265

Simplifying
y + -5.5 = -3.041381265

Reorder the terms:
-5.5 + y = -3.041381265

Solving
-5.5 + y = -3.041381265

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 = -3.041381265 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = -3.041381265 + 5.5
y = -3.041381265 + 5.5

Combine like terms: -3.041381265 + 5.5 = 2.458618735
y = 2.458618735

Simplifying
y = 2.458618735


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.541381265, 2.458618735}

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