y^2-2y+1=2.25

Solution for y^2-2y+1=2.25 equation:

Simplifying
y2 + -2y + 1 = 2.25

Reorder the terms:
1 + -2y + y2 = 2.25

Solving
1 + -2y + y2 = 2.25

Solving for variable 'y'.

Reorder the terms:
1 + -2.25 + -2y + y2 = 2.25 + -2.25

Combine like terms: 1 + -2.25 = -1.25
-1.25 + -2y + y2 = 2.25 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
-1.25 + -2y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -2y + 1.25 + y2 = 0.00 + 1.25

Reorder the terms:
-1.25 + 1.25 + -2y + y2 = 0.00 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -2y + y2 = 0.00 + 1.25
-2y + y2 = 0.00 + 1.25

Combine like terms: 0.00 + 1.25 = 1.25
-2y + y2 = 1.25

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 = 1.25 + 1

Reorder the terms:
1 + -2y + y2 = 1.25 + 1

Combine like terms: 1.25 + 1 = 2.25
1 + -2y + y2 = 2.25

Factor a perfect square on the left side:
(y + -1)(y + -1) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(y + -1) equal to 1.5 and -1.5.

Subproblem 1
y + -1 = 1.5

Simplifying
y + -1 = 1.5

Reorder the terms:
-1 + y = 1.5

Solving
-1 + y = 1.5

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 = 1.5 + 1

Combine like terms: -1 + 1 = 0
0 + y = 1.5 + 1
y = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
y = 2.5

Simplifying
y = 2.5

Subproblem 2
y + -1 = -1.5

Simplifying
y + -1 = -1.5

Reorder the terms:
-1 + y = -1.5

Solving
-1 + y = -1.5

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 = -1.5 + 1

Combine like terms: -1 + 1 = 0
0 + y = -1.5 + 1
y = -1.5 + 1

Combine like terms: -1.5 + 1 = -0.5
y = -0.5

Simplifying
y = -0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.5, -0.5}