y(y+4)=1

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Solution for y(y+4)=1 equation: 


Simplifying
y(y + 4) = 1

Reorder the terms:
y(4 + y) = 1
(4 * y + y * y) = 1
(4y + y2) = 1

Solving
4y + y2 = 1

Solving for variable 'y'.

Reorder the terms:
-1 + 4y + y2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + 4y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4y + y2 = 0 + 1
4y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
4y + y2 = 1

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 1 + 4

Reorder the terms:
4 + 4y + y2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + 4y + y2 = 5

Factor a perfect square on the left side:
(y + 2)(y + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(y + 2) equal to 2.236067978 and -2.236067978.


Subproblem 1
y + 2 = 2.236067978

Simplifying
y + 2 = 2.236067978

Reorder the terms:
2 + y = 2.236067978

Solving
2 + y = 2.236067978

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = 2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + y = 2.236067978 + -2
y = 2.236067978 + -2

Combine like terms: 2.236067978 + -2 = 0.236067978
y = 0.236067978

Simplifying
y = 0.236067978


Subproblem 2
y + 2 = -2.236067978

Simplifying
y + 2 = -2.236067978

Reorder the terms:
2 + y = -2.236067978

Solving
2 + y = -2.236067978

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = -2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + y = -2.236067978 + -2
y = -2.236067978 + -2

Combine like terms: -2.236067978 + -2 = -4.236067978
y = -4.236067978

Simplifying
y = -4.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.236067978, -4.236067978}

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