y^2-2y=2.5

Solution for y^2-2y=2.5 equation:

Simplifying
y2 + -2y = 2.5

Reorder the terms:
-2y + y2 = 2.5

Solving
-2y + y2 = 2.5

Solving for variable 'y'.

Reorder the terms:
-2.5 + -2y + y2 = 2.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
-2.5 + -2y + y2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -2y + 2.5 + y2 = 0.0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -2y + y2 = 0.0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -2y + y2 = 0.0 + 2.5
-2y + y2 = 0.0 + 2.5

Combine like terms: 0.0 + 2.5 = 2.5
-2y + y2 = 2.5

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 = 2.5 + 1

Reorder the terms:
1 + -2y + y2 = 2.5 + 1

Combine like terms: 2.5 + 1 = 3.5
1 + -2y + y2 = 3.5

Factor a perfect square on the left side:
(y + -1)(y + -1) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(y + -1) equal to 1.870828693 and -1.870828693.

Subproblem 1
y + -1 = 1.870828693

Simplifying
y + -1 = 1.870828693

Reorder the terms:
-1 + y = 1.870828693

Solving
-1 + y = 1.870828693

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 = 1.870828693 + 1

Combine like terms: -1 + 1 = 0
0 + y = 1.870828693 + 1
y = 1.870828693 + 1

Combine like terms: 1.870828693 + 1 = 2.870828693
y = 2.870828693

Simplifying
y = 2.870828693

Subproblem 2
y + -1 = -1.870828693

Simplifying
y + -1 = -1.870828693

Reorder the terms:
-1 + y = -1.870828693

Solving
-1 + y = -1.870828693

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 = -1.870828693 + 1

Combine like terms: -1 + 1 = 0
0 + y = -1.870828693 + 1
y = -1.870828693 + 1

Combine like terms: -1.870828693 + 1 = -0.870828693
y = -0.870828693

Simplifying
y = -0.870828693

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.870828693, -0.870828693}