0=-y^2-2y+30

Solution for 0=-y^2-2y+30 equation:

Simplifying
0 = -1y2 + -2y + 30

Reorder the terms:
0 = 30 + -2y + -1y2

Solving
0 = 30 + -2y + -1y2

Solving for variable 'y'.

Combine like terms: 0 + -30 = -30
-30 + 2y + y2 = 30 + -2y + -1y2 + -30 + 2y + y2

Reorder the terms:
-30 + 2y + y2 = 30 + -30 + -2y + 2y + -1y2 + y2

Combine like terms: 30 + -30 = 0
-30 + 2y + y2 = 0 + -2y + 2y + -1y2 + y2
-30 + 2y + y2 = -2y + 2y + -1y2 + y2

Combine like terms: -2y + 2y = 0
-30 + 2y + y2 = 0 + -1y2 + y2
-30 + 2y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-30 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2y + 30 + y2 = 0 + 30

Reorder the terms:
-30 + 30 + 2y + y2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2y + y2 = 0 + 30
2y + y2 = 0 + 30

Combine like terms: 0 + 30 = 30
2y + y2 = 30

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 = 30 + 1

Reorder the terms:
1 + 2y + y2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + 2y + y2 = 31

Factor a perfect square on the left side:
(y + 1)(y + 1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(y + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1
y + 1 = 5.567764363

Simplifying
y + 1 = 5.567764363

Reorder the terms:
1 + y = 5.567764363

Solving
1 + y = 5.567764363

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 = 5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + y = 5.567764363 + -1
y = 5.567764363 + -1

Combine like terms: 5.567764363 + -1 = 4.567764363
y = 4.567764363

Simplifying
y = 4.567764363

Subproblem 2
y + 1 = -5.567764363

Simplifying
y + 1 = -5.567764363

Reorder the terms:
1 + y = -5.567764363

Solving
1 + y = -5.567764363

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 = -5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + y = -5.567764363 + -1
y = -5.567764363 + -1

Combine like terms: -5.567764363 + -1 = -6.567764363
y = -6.567764363

Simplifying
y = -6.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.567764363, -6.567764363}