2y^2+3y-29=(y+1)2

Solution for 2y^2+3y-29=(y+1)2 equation:

Simplifying
2y2 + 3y + -29 = (y + 1) * 2

Reorder the terms:
-29 + 3y + 2y2 = (y + 1) * 2

Reorder the terms:
-29 + 3y + 2y2 = (1 + y) * 2

Reorder the terms for easier multiplication:
-29 + 3y + 2y2 = 2(1 + y)
-29 + 3y + 2y2 = (1 * 2 + y * 2)
-29 + 3y + 2y2 = (2 + 2y)

Solving
-29 + 3y + 2y2 = 2 + 2y

Solving for variable 'y'.

Reorder the terms:
-29 + -2 + 3y + -2y + 2y2 = 2 + 2y + -2 + -2y

Combine like terms: -29 + -2 = -31
-31 + 3y + -2y + 2y2 = 2 + 2y + -2 + -2y

Combine like terms: 3y + -2y = 1y
-31 + 1y + 2y2 = 2 + 2y + -2 + -2y

Reorder the terms:
-31 + 1y + 2y2 = 2 + -2 + 2y + -2y

Combine like terms: 2 + -2 = 0
-31 + 1y + 2y2 = 0 + 2y + -2y
-31 + 1y + 2y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-31 + 1y + 2y2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-15.5 + 0.5y + y2 = 0

Move the constant term to the right:

Add '15.5' to each side of the equation.
-15.5 + 0.5y + 15.5 + y2 = 0 + 15.5

Reorder the terms:
-15.5 + 15.5 + 0.5y + y2 = 0 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + 0.5y + y2 = 0 + 15.5
0.5y + y2 = 0 + 15.5

Combine like terms: 0 + 15.5 = 15.5
0.5y + y2 = 15.5

The y term is 0.5y.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5y + 0.0625 + y2 = 15.5 + 0.0625

Reorder the terms:
0.0625 + 0.5y + y2 = 15.5 + 0.0625

Combine like terms: 15.5 + 0.0625 = 15.5625
0.0625 + 0.5y + y2 = 15.5625

Factor a perfect square on the left side:
(y + 0.25)(y + 0.25) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(y + 0.25) equal to 3.94493346 and -3.94493346.

Subproblem 1
y + 0.25 = 3.94493346

Simplifying
y + 0.25 = 3.94493346

Reorder the terms:
0.25 + y = 3.94493346

Solving
0.25 + y = 3.94493346

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = 3.94493346 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = 3.94493346 + -0.25
y = 3.94493346 + -0.25

Combine like terms: 3.94493346 + -0.25 = 3.69493346
y = 3.69493346

Simplifying
y = 3.69493346

Subproblem 2
y + 0.25 = -3.94493346

Simplifying
y + 0.25 = -3.94493346

Reorder the terms:
0.25 + y = -3.94493346

Solving
0.25 + y = -3.94493346

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = -3.94493346 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = -3.94493346 + -0.25
y = -3.94493346 + -0.25

Combine like terms: -3.94493346 + -0.25 = -4.19493346
y = -4.19493346

Simplifying
y = -4.19493346

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.69493346, -4.19493346}