y(y+2)=67.89

Solution for y(y+2)=67.89 equation:

Simplifying
y(y + 2) = 67.89

Reorder the terms:
y(2 + y) = 67.89
(2 * y + y * y) = 67.89
(2y + y2) = 67.89

Solving
2y + y2 = 67.89

Solving for variable 'y'.

Reorder the terms:
-67.89 + 2y + y2 = 67.89 + -67.89

Combine like terms: 67.89 + -67.89 = 0.00
-67.89 + 2y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '67.89' to each side of the equation.
-67.89 + 2y + 67.89 + y2 = 0.00 + 67.89

Reorder the terms:
-67.89 + 67.89 + 2y + y2 = 0.00 + 67.89

Combine like terms: -67.89 + 67.89 = 0.00
0.00 + 2y + y2 = 0.00 + 67.89
2y + y2 = 0.00 + 67.89

Combine like terms: 0.00 + 67.89 = 67.89
2y + y2 = 67.89

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 = 67.89 + 1

Reorder the terms:
1 + 2y + y2 = 67.89 + 1

Combine like terms: 67.89 + 1 = 68.89
1 + 2y + y2 = 68.89

Factor a perfect square on the left side:
(y + 1)(y + 1) = 68.89

Calculate the square root of the right side: 8.3

Break this problem into two subproblems by setting 
(y + 1) equal to 8.3 and -8.3.

Subproblem 1
y + 1 = 8.3

Simplifying
y + 1 = 8.3

Reorder the terms:
1 + y = 8.3

Solving
1 + y = 8.3

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 = 8.3 + -1

Combine like terms: 1 + -1 = 0
0 + y = 8.3 + -1
y = 8.3 + -1

Combine like terms: 8.3 + -1 = 7.3
y = 7.3

Simplifying
y = 7.3

Subproblem 2
y + 1 = -8.3

Simplifying
y + 1 = -8.3

Reorder the terms:
1 + y = -8.3

Solving
1 + y = -8.3

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 = -8.3 + -1

Combine like terms: 1 + -1 = 0
0 + y = -8.3 + -1
y = -8.3 + -1

Combine like terms: -8.3 + -1 = -9.3
y = -9.3

Simplifying
y = -9.3

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.3, -9.3}