y^2-4y-20=3+2

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Solution for y^2-4y-20=3+2 equation: 


Simplifying
y2 + -4y + -20 = 3 + 2

Reorder the terms:
-20 + -4y + y2 = 3 + 2

Combine like terms: 3 + 2 = 5
-20 + -4y + y2 = 5

Solving
-20 + -4y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
-20 + -5 + -4y + y2 = 5 + -5

Combine like terms: -20 + -5 = -25
-25 + -4y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-25 + -4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -4y + 25 + y2 = 0 + 25

Reorder the terms:
-25 + 25 + -4y + y2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -4y + y2 = 0 + 25
-4y + y2 = 0 + 25

Combine like terms: 0 + 25 = 25
-4y + y2 = 25

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 25 + 4

Reorder the terms:
4 + -4y + y2 = 25 + 4

Combine like terms: 25 + 4 = 29
4 + -4y + y2 = 29

Factor a perfect square on the left side:
(y + -2)(y + -2) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(y + -2) equal to 5.385164807 and -5.385164807.


Subproblem 1
y + -2 = 5.385164807

Simplifying
y + -2 = 5.385164807

Reorder the terms:
-2 + y = 5.385164807

Solving
-2 + y = 5.385164807

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 5.385164807 + 2

Combine like terms: -2 + 2 = 0
0 + y = 5.385164807 + 2
y = 5.385164807 + 2

Combine like terms: 5.385164807 + 2 = 7.385164807
y = 7.385164807

Simplifying
y = 7.385164807


Subproblem 2
y + -2 = -5.385164807

Simplifying
y + -2 = -5.385164807

Reorder the terms:
-2 + y = -5.385164807

Solving
-2 + y = -5.385164807

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -5.385164807 + 2

Combine like terms: -2 + 2 = 0
0 + y = -5.385164807 + 2
y = -5.385164807 + 2

Combine like terms: -5.385164807 + 2 = -3.385164807
y = -3.385164807

Simplifying
y = -3.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.385164807, -3.385164807}

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