y^2-20y+20=0

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Solution for y^2-20y+20=0 equation: 


Simplifying
y2 + -20y + 20 = 0

Reorder the terms:
20 + -20y + y2 = 0

Solving
20 + -20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -20y + -20 + y2 = 0 + -20

Reorder the terms:
20 + -20 + -20y + y2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -20y + y2 = 0 + -20
-20y + y2 = 0 + -20

Combine like terms: 0 + -20 = -20
-20y + y2 = -20

The y term is -20y.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20y + 100 + y2 = -20 + 100

Reorder the terms:
100 + -20y + y2 = -20 + 100

Combine like terms: -20 + 100 = 80
100 + -20y + y2 = 80

Factor a perfect square on the left side:
(y + -10)(y + -10) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(y + -10) equal to 8.94427191 and -8.94427191.


Subproblem 1
y + -10 = 8.94427191

Simplifying
y + -10 = 8.94427191

Reorder the terms:
-10 + y = 8.94427191

Solving
-10 + y = 8.94427191

Solving for variable 'y'.

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

Add '10' to each side of the equation.
-10 + 10 + y = 8.94427191 + 10

Combine like terms: -10 + 10 = 0
0 + y = 8.94427191 + 10
y = 8.94427191 + 10

Combine like terms: 8.94427191 + 10 = 18.94427191
y = 18.94427191

Simplifying
y = 18.94427191


Subproblem 2
y + -10 = -8.94427191

Simplifying
y + -10 = -8.94427191

Reorder the terms:
-10 + y = -8.94427191

Solving
-10 + y = -8.94427191

Solving for variable 'y'.

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

Add '10' to each side of the equation.
-10 + 10 + y = -8.94427191 + 10

Combine like terms: -10 + 10 = 0
0 + y = -8.94427191 + 10
y = -8.94427191 + 10

Combine like terms: -8.94427191 + 10 = 1.05572809
y = 1.05572809

Simplifying
y = 1.05572809


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {18.94427191, 1.05572809}

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