y^2-2y-27=0

Solution for y^2-2y-27=0 equation:

Simplifying
y2 + -2y + -27 = 0

Reorder the terms:
-27 + -2y + y2 = 0

Solving
-27 + -2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -2y + 27 + y2 = 0 + 27

Reorder the terms:
-27 + 27 + -2y + y2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2y + y2 = 0 + 27
-2y + y2 = 0 + 27

Combine like terms: 0 + 27 = 27
-2y + y2 = 27

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 = 27 + 1

Reorder the terms:
1 + -2y + y2 = 27 + 1

Combine like terms: 27 + 1 = 28
1 + -2y + y2 = 28

Factor a perfect square on the left side:
(y + -1)(y + -1) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(y + -1) equal to 5.291502622 and -5.291502622.

Subproblem 1
y + -1 = 5.291502622

Simplifying
y + -1 = 5.291502622

Reorder the terms:
-1 + y = 5.291502622

Solving
-1 + y = 5.291502622

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 = 5.291502622 + 1

Combine like terms: -1 + 1 = 0
0 + y = 5.291502622 + 1
y = 5.291502622 + 1

Combine like terms: 5.291502622 + 1 = 6.291502622
y = 6.291502622

Simplifying
y = 6.291502622

Subproblem 2
y + -1 = -5.291502622

Simplifying
y + -1 = -5.291502622

Reorder the terms:
-1 + y = -5.291502622

Solving
-1 + y = -5.291502622

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 = -5.291502622 + 1

Combine like terms: -1 + 1 = 0
0 + y = -5.291502622 + 1
y = -5.291502622 + 1

Combine like terms: -5.291502622 + 1 = -4.291502622
y = -4.291502622

Simplifying
y = -4.291502622

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.291502622, -4.291502622}