y^2-7y+11=0

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Solution for y^2-7y+11=0 equation: 


Simplifying
y2 + -7y + 11 = 0

Reorder the terms:
11 + -7y + y2 = 0

Solving
11 + -7y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -7y + -11 + y2 = 0 + -11

Reorder the terms:
11 + -11 + -7y + y2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -7y + y2 = 0 + -11
-7y + y2 = 0 + -11

Combine like terms: 0 + -11 = -11
-7y + y2 = -11

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = -11 + 12.25

Reorder the terms:
12.25 + -7y + y2 = -11 + 12.25

Combine like terms: -11 + 12.25 = 1.25
12.25 + -7y + y2 = 1.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(y + -3.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
y + -3.5 = 1.118033989

Simplifying
y + -3.5 = 1.118033989

Reorder the terms:
-3.5 + y = 1.118033989

Solving
-3.5 + y = 1.118033989

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = 1.118033989 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 1.118033989 + 3.5
y = 1.118033989 + 3.5

Combine like terms: 1.118033989 + 3.5 = 4.618033989
y = 4.618033989

Simplifying
y = 4.618033989


Subproblem 2
y + -3.5 = -1.118033989

Simplifying
y + -3.5 = -1.118033989

Reorder the terms:
-3.5 + y = -1.118033989

Solving
-3.5 + y = -1.118033989

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = -1.118033989 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -1.118033989 + 3.5
y = -1.118033989 + 3.5

Combine like terms: -1.118033989 + 3.5 = 2.381966011
y = 2.381966011

Simplifying
y = 2.381966011


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.618033989, 2.381966011}

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