y^2-21y-20=0

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Solution for y^2-21y-20=0 equation: 


Simplifying
y2 + -21y + -20 = 0

Reorder the terms:
-20 + -21y + y2 = 0

Solving
-20 + -21y + 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 + -21y + 20 + y2 = 0 + 20

Reorder the terms:
-20 + 20 + -21y + y2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -21y + y2 = 0 + 20
-21y + y2 = 0 + 20

Combine like terms: 0 + 20 = 20
-21y + y2 = 20

The y term is -21y.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21y + 110.25 + y2 = 20 + 110.25

Reorder the terms:
110.25 + -21y + y2 = 20 + 110.25

Combine like terms: 20 + 110.25 = 130.25
110.25 + -21y + y2 = 130.25

Factor a perfect square on the left side:
(y + -10.5)(y + -10.5) = 130.25

Calculate the square root of the right side: 11.412712211

Break this problem into two subproblems by setting 
(y + -10.5) equal to 11.412712211 and -11.412712211.


Subproblem 1
y + -10.5 = 11.412712211

Simplifying
y + -10.5 = 11.412712211

Reorder the terms:
-10.5 + y = 11.412712211

Solving
-10.5 + y = 11.412712211

Solving for variable 'y'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + y = 11.412712211 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + y = 11.412712211 + 10.5
y = 11.412712211 + 10.5

Combine like terms: 11.412712211 + 10.5 = 21.912712211
y = 21.912712211

Simplifying
y = 21.912712211


Subproblem 2
y + -10.5 = -11.412712211

Simplifying
y + -10.5 = -11.412712211

Reorder the terms:
-10.5 + y = -11.412712211

Solving
-10.5 + y = -11.412712211

Solving for variable 'y'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + y = -11.412712211 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + y = -11.412712211 + 10.5
y = -11.412712211 + 10.5

Combine like terms: -11.412712211 + 10.5 = -0.912712211
y = -0.912712211

Simplifying
y = -0.912712211


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {21.912712211, -0.912712211}

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