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

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


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

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

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

Remove parenthesis around (1 + y)
-29 + 3y + 2y2 = 1 + y

Solving
-29 + 3y + 2y2 = 1 + y

Solving for variable 'y'.

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

Combine like terms: -29 + -1 = -30
-30 + 3y + -1y + 2y2 = 1 + y + -1 + -1y

Combine like terms: 3y + -1y = 2y
-30 + 2y + 2y2 = 1 + y + -1 + -1y

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + y + y2)' equal to zero and attempt to solve:

Simplifying
-15 + y + y2 = 0

Solving
-15 + y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + y + 15 + y2 = 0 + 15

Reorder the terms:
-15 + 15 + y + y2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + y + y2 = 0 + 15
y + y2 = 0 + 15

Combine like terms: 0 + 15 = 15
y + y2 = 15

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

Add '0.25' to each side of the equation.
y + 0.25 + y2 = 15 + 0.25

Reorder the terms:
0.25 + y + y2 = 15 + 0.25

Combine like terms: 15 + 0.25 = 15.25
0.25 + y + y2 = 15.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(y + 0.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
y + 0.5 = 3.905124838

Simplifying
y + 0.5 = 3.905124838

Reorder the terms:
0.5 + y = 3.905124838

Solving
0.5 + y = 3.905124838

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 3.905124838 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 3.905124838 + -0.5
y = 3.905124838 + -0.5

Combine like terms: 3.905124838 + -0.5 = 3.405124838
y = 3.405124838

Simplifying
y = 3.405124838


Subproblem 2
y + 0.5 = -3.905124838

Simplifying
y + 0.5 = -3.905124838

Reorder the terms:
0.5 + y = -3.905124838

Solving
0.5 + y = -3.905124838

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -3.905124838 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -3.905124838 + -0.5
y = -3.905124838 + -0.5

Combine like terms: -3.905124838 + -0.5 = -4.405124838
y = -4.405124838

Simplifying
y = -4.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.405124838, -4.405124838}
Solution
y = {3.405124838, -4.405124838}

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