y^2-20y+4=0

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Solution for y^2-20y+4=0 equation: 


Simplifying
y2 + -20y + 4 = 0

Reorder the terms:
4 + -20y + y2 = 0

Solving
4 + -20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -20y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + -20y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -20y + y2 = 0 + -4
-20y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
-20y + y2 = -4

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 = -4 + 100

Reorder the terms:
100 + -20y + y2 = -4 + 100

Combine like terms: -4 + 100 = 96
100 + -20y + y2 = 96

Factor a perfect square on the left side:
(y + -10)(y + -10) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(y + -10) equal to 9.797958971 and -9.797958971.


Subproblem 1
y + -10 = 9.797958971

Simplifying
y + -10 = 9.797958971

Reorder the terms:
-10 + y = 9.797958971

Solving
-10 + y = 9.797958971

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 = 9.797958971 + 10

Combine like terms: -10 + 10 = 0
0 + y = 9.797958971 + 10
y = 9.797958971 + 10

Combine like terms: 9.797958971 + 10 = 19.797958971
y = 19.797958971

Simplifying
y = 19.797958971


Subproblem 2
y + -10 = -9.797958971

Simplifying
y + -10 = -9.797958971

Reorder the terms:
-10 + y = -9.797958971

Solving
-10 + y = -9.797958971

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 = -9.797958971 + 10

Combine like terms: -10 + 10 = 0
0 + y = -9.797958971 + 10
y = -9.797958971 + 10

Combine like terms: -9.797958971 + 10 = 0.202041029
y = 0.202041029

Simplifying
y = 0.202041029


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {19.797958971, 0.202041029}

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