y^2-2y-64=0

Solution for y^2-2y-64=0 equation:

Simplifying
y2 + -2y + -64 = 0

Reorder the terms:
-64 + -2y + y2 = 0

Solving
-64 + -2y + 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 + -2y + 64 + y2 = 0 + 64

Reorder the terms:
-64 + 64 + -2y + y2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -2y + y2 = 0 + 64
-2y + y2 = 0 + 64

Combine like terms: 0 + 64 = 64
-2y + y2 = 64

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 64 + 1

Reorder the terms:
1 + -2y + y2 = 64 + 1

Combine like terms: 64 + 1 = 65
1 + -2y + y2 = 65

Factor a perfect square on the left side:
(y + -1)(y + -1) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(y + -1) equal to 8.062257748 and -8.062257748.

Subproblem 1
y + -1 = 8.062257748

Simplifying
y + -1 = 8.062257748

Reorder the terms:
-1 + y = 8.062257748

Solving
-1 + y = 8.062257748

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 8.062257748 + 1

Combine like terms: -1 + 1 = 0
0 + y = 8.062257748 + 1
y = 8.062257748 + 1

Combine like terms: 8.062257748 + 1 = 9.062257748
y = 9.062257748

Simplifying
y = 9.062257748

Subproblem 2
y + -1 = -8.062257748

Simplifying
y + -1 = -8.062257748

Reorder the terms:
-1 + y = -8.062257748

Solving
-1 + y = -8.062257748

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -8.062257748 + 1

Combine like terms: -1 + 1 = 0
0 + y = -8.062257748 + 1
y = -8.062257748 + 1

Combine like terms: -8.062257748 + 1 = -7.062257748
y = -7.062257748

Simplifying
y = -7.062257748

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.062257748, -7.062257748}