y^2-2y-2500=0

Solution for y^2-2y-2500=0 equation:

Simplifying
y2 + -2y + -2500 = 0

Reorder the terms:
-2500 + -2y + y2 = 0

Solving
-2500 + -2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '2500' to each side of the equation.
-2500 + -2y + 2500 + y2 = 0 + 2500

Reorder the terms:
-2500 + 2500 + -2y + y2 = 0 + 2500

Combine like terms: -2500 + 2500 = 0
0 + -2y + y2 = 0 + 2500
-2y + y2 = 0 + 2500

Combine like terms: 0 + 2500 = 2500
-2y + y2 = 2500

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 = 2500 + 1

Reorder the terms:
1 + -2y + y2 = 2500 + 1

Combine like terms: 2500 + 1 = 2501
1 + -2y + y2 = 2501

Factor a perfect square on the left side:
(y + -1)(y + -1) = 2501

Calculate the square root of the right side: 50.009999

Break this problem into two subproblems by setting 
(y + -1) equal to 50.009999 and -50.009999.

Subproblem 1
y + -1 = 50.009999

Simplifying
y + -1 = 50.009999

Reorder the terms:
-1 + y = 50.009999

Solving
-1 + y = 50.009999

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 = 50.009999 + 1

Combine like terms: -1 + 1 = 0
0 + y = 50.009999 + 1
y = 50.009999 + 1

Combine like terms: 50.009999 + 1 = 51.009999
y = 51.009999

Simplifying
y = 51.009999

Subproblem 2
y + -1 = -50.009999

Simplifying
y + -1 = -50.009999

Reorder the terms:
-1 + y = -50.009999

Solving
-1 + y = -50.009999

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 = -50.009999 + 1

Combine like terms: -1 + 1 = 0
0 + y = -50.009999 + 1
y = -50.009999 + 1

Combine like terms: -50.009999 + 1 = -49.009999
y = -49.009999

Simplifying
y = -49.009999

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {51.009999, -49.009999}