y^2+8y+13=0

Solution for y^2+8y+13=0 equation:

Simplifying
y2 + 8y + 13 = 0

Reorder the terms:
13 + 8y + y2 = 0

Solving
13 + 8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 8y + -13 + y2 = 0 + -13

Reorder the terms:
13 + -13 + 8y + y2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 8y + y2 = 0 + -13
8y + y2 = 0 + -13

Combine like terms: 0 + -13 = -13
8y + y2 = -13

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 = -13 + 16

Reorder the terms:
16 + 8y + y2 = -13 + 16

Combine like terms: -13 + 16 = 3
16 + 8y + y2 = 3

Factor a perfect square on the left side:
(y + 4)(y + 4) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + 4) equal to 1.732050808 and -1.732050808.

Subproblem 1
y + 4 = 1.732050808

Simplifying
y + 4 = 1.732050808

Reorder the terms:
4 + y = 1.732050808

Solving
4 + y = 1.732050808

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 = 1.732050808 + -4

Combine like terms: 4 + -4 = 0
0 + y = 1.732050808 + -4
y = 1.732050808 + -4

Combine like terms: 1.732050808 + -4 = -2.267949192
y = -2.267949192

Simplifying
y = -2.267949192

Subproblem 2
y + 4 = -1.732050808

Simplifying
y + 4 = -1.732050808

Reorder the terms:
4 + y = -1.732050808

Solving
4 + y = -1.732050808

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 = -1.732050808 + -4

Combine like terms: 4 + -4 = 0
0 + y = -1.732050808 + -4
y = -1.732050808 + -4

Combine like terms: -1.732050808 + -4 = -5.732050808
y = -5.732050808

Simplifying
y = -5.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.267949192, -5.732050808}