y^2+8y=-11

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Solution for y^2+8y=-11 equation: 


Simplifying
y2 + 8y = -11

Reorder the terms:
8y + y2 = -11

Solving
8y + y2 = -11

Solving for variable 'y'.

Reorder the terms:
11 + 8y + y2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 8y + -11 + y2 = 0 + -11

Reorder the terms:
11 + -11 + 8y + y2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 8y + y2 = 0 + -11
8y + y2 = 0 + -11

Combine like terms: 0 + -11 = -11
8y + y2 = -11

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = -11 + 16

Reorder the terms:
16 + 8y + y2 = -11 + 16

Combine like terms: -11 + 16 = 5
16 + 8y + y2 = 5

Factor a perfect square on the left side:
(y + 4)(y + 4) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(y + 4) equal to 2.236067978 and -2.236067978.


Subproblem 1
y + 4 = 2.236067978

Simplifying
y + 4 = 2.236067978

Reorder the terms:
4 + y = 2.236067978

Solving
4 + y = 2.236067978

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 2.236067978 + -4

Combine like terms: 4 + -4 = 0
0 + y = 2.236067978 + -4
y = 2.236067978 + -4

Combine like terms: 2.236067978 + -4 = -1.763932022
y = -1.763932022

Simplifying
y = -1.763932022


Subproblem 2
y + 4 = -2.236067978

Simplifying
y + 4 = -2.236067978

Reorder the terms:
4 + y = -2.236067978

Solving
4 + y = -2.236067978

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -2.236067978 + -4

Combine like terms: 4 + -4 = 0
0 + y = -2.236067978 + -4
y = -2.236067978 + -4

Combine like terms: -2.236067978 + -4 = -6.236067978
y = -6.236067978

Simplifying
y = -6.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.763932022, -6.236067978}

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