y^2+16y+13=0

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Solution for y^2+16y+13=0 equation: 


Simplifying
y2 + 16y + 13 = 0

Reorder the terms:
13 + 16y + y2 = 0

Solving
13 + 16y + 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 + 16y + -13 + y2 = 0 + -13

Reorder the terms:
13 + -13 + 16y + y2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 16y + y2 = 0 + -13
16y + y2 = 0 + -13

Combine like terms: 0 + -13 = -13
16y + y2 = -13

The y term is 16y.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16y + 64 + y2 = -13 + 64

Reorder the terms:
64 + 16y + y2 = -13 + 64

Combine like terms: -13 + 64 = 51
64 + 16y + y2 = 51

Factor a perfect square on the left side:
(y + 8)(y + 8) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(y + 8) equal to 7.141428429 and -7.141428429.


Subproblem 1
y + 8 = 7.141428429

Simplifying
y + 8 = 7.141428429

Reorder the terms:
8 + y = 7.141428429

Solving
8 + y = 7.141428429

Solving for variable 'y'.

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

Add '-8' to each side of the equation.
8 + -8 + y = 7.141428429 + -8

Combine like terms: 8 + -8 = 0
0 + y = 7.141428429 + -8
y = 7.141428429 + -8

Combine like terms: 7.141428429 + -8 = -0.858571571
y = -0.858571571

Simplifying
y = -0.858571571


Subproblem 2
y + 8 = -7.141428429

Simplifying
y + 8 = -7.141428429

Reorder the terms:
8 + y = -7.141428429

Solving
8 + y = -7.141428429

Solving for variable 'y'.

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

Add '-8' to each side of the equation.
8 + -8 + y = -7.141428429 + -8

Combine like terms: 8 + -8 = 0
0 + y = -7.141428429 + -8
y = -7.141428429 + -8

Combine like terms: -7.141428429 + -8 = -15.141428429
y = -15.141428429

Simplifying
y = -15.141428429


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.858571571, -15.141428429}

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