4y+29=2y^2

Solution for 4y+29=2y^2 equation:

Simplifying
4y + 29 = 2y2

Reorder the terms:
29 + 4y = 2y2

Solving
29 + 4y = 2y2

Solving for variable 'y'.

Combine like terms: 2y2 + -2y2 = 0
29 + 4y + -2y2 = 0

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

Divide each side by '-2'.
-14.5 + -2y + y2 = 0

Move the constant term to the right:

Add '14.5' to each side of the equation.
-14.5 + -2y + 14.5 + y2 = 0 + 14.5

Reorder the terms:
-14.5 + 14.5 + -2y + y2 = 0 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + -2y + y2 = 0 + 14.5
-2y + y2 = 0 + 14.5

Combine like terms: 0 + 14.5 = 14.5
-2y + y2 = 14.5

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 = 14.5 + 1

Reorder the terms:
1 + -2y + y2 = 14.5 + 1

Combine like terms: 14.5 + 1 = 15.5
1 + -2y + y2 = 15.5

Factor a perfect square on the left side:
(y + -1)(y + -1) = 15.5

Calculate the square root of the right side: 3.937003937

Break this problem into two subproblems by setting 
(y + -1) equal to 3.937003937 and -3.937003937.

Subproblem 1
y + -1 = 3.937003937

Simplifying
y + -1 = 3.937003937

Reorder the terms:
-1 + y = 3.937003937

Solving
-1 + y = 3.937003937

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 = 3.937003937 + 1

Combine like terms: -1 + 1 = 0
0 + y = 3.937003937 + 1
y = 3.937003937 + 1

Combine like terms: 3.937003937 + 1 = 4.937003937
y = 4.937003937

Simplifying
y = 4.937003937

Subproblem 2
y + -1 = -3.937003937

Simplifying
y + -1 = -3.937003937

Reorder the terms:
-1 + y = -3.937003937

Solving
-1 + y = -3.937003937

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 = -3.937003937 + 1

Combine like terms: -1 + 1 = 0
0 + y = -3.937003937 + 1
y = -3.937003937 + 1

Combine like terms: -3.937003937 + 1 = -2.937003937
y = -2.937003937

Simplifying
y = -2.937003937

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.937003937, -2.937003937}