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 = 120
100 + -20y + y2 = 120

Factor a perfect square on the left side:
(y + -10)(y + -10) = 120

Calculate the square root of the right side: 10.95445115

Break this problem into two subproblems by setting 
(y + -10) equal to 10.95445115 and -10.95445115.


Subproblem 1
y + -10 = 10.95445115

Simplifying
y + -10 = 10.95445115

Reorder the terms:
-10 + y = 10.95445115

Solving
-10 + y = 10.95445115

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 = 10.95445115 + 10

Combine like terms: -10 + 10 = 0
0 + y = 10.95445115 + 10
y = 10.95445115 + 10

Combine like terms: 10.95445115 + 10 = 20.95445115
y = 20.95445115

Simplifying
y = 20.95445115


Subproblem 2
y + -10 = -10.95445115

Simplifying
y + -10 = -10.95445115

Reorder the terms:
-10 + y = -10.95445115

Solving
-10 + y = -10.95445115

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 = -10.95445115 + 10

Combine like terms: -10 + 10 = 0
0 + y = -10.95445115 + 10
y = -10.95445115 + 10

Combine like terms: -10.95445115 + 10 = -0.95445115
y = -0.95445115

Simplifying
y = -0.95445115


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {20.95445115, -0.95445115}

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