y^2-10y+11=0

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Solution for y^2-10y+11=0 equation: 


Simplifying
y2 + -10y + 11 = 0

Reorder the terms:
11 + -10y + y2 = 0

Solving
11 + -10y + 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 + -10y + -11 + y2 = 0 + -11

Reorder the terms:
11 + -11 + -10y + y2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -10y + y2 = 0 + -11
-10y + y2 = 0 + -11

Combine like terms: 0 + -11 = -11
-10y + y2 = -11

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = -11 + 25

Reorder the terms:
25 + -10y + y2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + -10y + y2 = 14

Factor a perfect square on the left side:
(y + -5)(y + -5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(y + -5) equal to 3.741657387 and -3.741657387.


Subproblem 1
y + -5 = 3.741657387

Simplifying
y + -5 = 3.741657387

Reorder the terms:
-5 + y = 3.741657387

Solving
-5 + y = 3.741657387

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = 3.741657387 + 5

Combine like terms: -5 + 5 = 0
0 + y = 3.741657387 + 5
y = 3.741657387 + 5

Combine like terms: 3.741657387 + 5 = 8.741657387
y = 8.741657387

Simplifying
y = 8.741657387


Subproblem 2
y + -5 = -3.741657387

Simplifying
y + -5 = -3.741657387

Reorder the terms:
-5 + y = -3.741657387

Solving
-5 + y = -3.741657387

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = -3.741657387 + 5

Combine like terms: -5 + 5 = 0
0 + y = -3.741657387 + 5
y = -3.741657387 + 5

Combine like terms: -3.741657387 + 5 = 1.258342613
y = 1.258342613

Simplifying
y = 1.258342613


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.741657387, 1.258342613}

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