Y^2+13Y-64=0

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Solution for Y^2+13Y-64=0 equation: 


Simplifying
Y2 + 13Y + -64 = 0

Reorder the terms:
-64 + 13Y + Y2 = 0

Solving
-64 + 13Y + Y2 = 0

Solving for variable 'Y'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 13Y + 64 + Y2 = 0 + 64

Reorder the terms:
-64 + 64 + 13Y + Y2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 13Y + Y2 = 0 + 64
13Y + Y2 = 0 + 64

Combine like terms: 0 + 64 = 64
13Y + Y2 = 64

The Y term is 13Y.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13Y + 42.25 + Y2 = 64 + 42.25

Reorder the terms:
42.25 + 13Y + Y2 = 64 + 42.25

Combine like terms: 64 + 42.25 = 106.25
42.25 + 13Y + Y2 = 106.25

Factor a perfect square on the left side:
(Y + 6.5)(Y + 6.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(Y + 6.5) equal to 10.307764064 and -10.307764064.


Subproblem 1
Y + 6.5 = 10.307764064

Simplifying
Y + 6.5 = 10.307764064

Reorder the terms:
6.5 + Y = 10.307764064

Solving
6.5 + Y = 10.307764064

Solving for variable 'Y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + Y = 10.307764064 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + Y = 10.307764064 + -6.5
Y = 10.307764064 + -6.5

Combine like terms: 10.307764064 + -6.5 = 3.807764064
Y = 3.807764064

Simplifying
Y = 3.807764064


Subproblem 2
Y + 6.5 = -10.307764064

Simplifying
Y + 6.5 = -10.307764064

Reorder the terms:
6.5 + Y = -10.307764064

Solving
6.5 + Y = -10.307764064

Solving for variable 'Y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + Y = -10.307764064 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + Y = -10.307764064 + -6.5
Y = -10.307764064 + -6.5

Combine like terms: -10.307764064 + -6.5 = -16.807764064
Y = -16.807764064

Simplifying
Y = -16.807764064


Solution
The solution to the problem is based on the solutions
from the subproblems.
Y = {3.807764064, -16.807764064}

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