y^2+2y+36=37

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Solution for y^2+2y+36=37 equation: 


Simplifying
y2 + 2y + 36 = 37

Reorder the terms:
36 + 2y + y2 = 37

Solving
36 + 2y + y2 = 37

Solving for variable 'y'.

Reorder the terms:
36 + -37 + 2y + y2 = 37 + -37

Combine like terms: 36 + -37 = -1
-1 + 2y + y2 = 37 + -37

Combine like terms: 37 + -37 = 0
-1 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2y + 1 + y2 = 0 + 1

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

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

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

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 = 1 + 1

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

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

Factor a perfect square on the left side:
(y + 1)(y + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + 1) equal to 1.414213562 and -1.414213562.


Subproblem 1
y + 1 = 1.414213562

Simplifying
y + 1 = 1.414213562

Reorder the terms:
1 + y = 1.414213562

Solving
1 + y = 1.414213562

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 = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + y = 1.414213562 + -1
y = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
y = 0.414213562

Simplifying
y = 0.414213562


Subproblem 2
y + 1 = -1.414213562

Simplifying
y + 1 = -1.414213562

Reorder the terms:
1 + y = -1.414213562

Solving
1 + y = -1.414213562

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 = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + y = -1.414213562 + -1
y = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
y = -2.414213562

Simplifying
y = -2.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.414213562, -2.414213562}

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