y^2+14y+5=0

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Solution for y^2+14y+5=0 equation: 


Simplifying
y2 + 14y + 5 = 0

Reorder the terms:
5 + 14y + y2 = 0

Solving
5 + 14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 14y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + 14y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 14y + y2 = 0 + -5
14y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
14y + y2 = -5

The y term is 14y.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14y + 49 + y2 = -5 + 49

Reorder the terms:
49 + 14y + y2 = -5 + 49

Combine like terms: -5 + 49 = 44
49 + 14y + y2 = 44

Factor a perfect square on the left side:
(y + 7)(y + 7) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(y + 7) equal to 6.633249581 and -6.633249581.


Subproblem 1
y + 7 = 6.633249581

Simplifying
y + 7 = 6.633249581

Reorder the terms:
7 + y = 6.633249581

Solving
7 + y = 6.633249581

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = 6.633249581 + -7

Combine like terms: 7 + -7 = 0
0 + y = 6.633249581 + -7
y = 6.633249581 + -7

Combine like terms: 6.633249581 + -7 = -0.366750419
y = -0.366750419

Simplifying
y = -0.366750419


Subproblem 2
y + 7 = -6.633249581

Simplifying
y + 7 = -6.633249581

Reorder the terms:
7 + y = -6.633249581

Solving
7 + y = -6.633249581

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = -6.633249581 + -7

Combine like terms: 7 + -7 = 0
0 + y = -6.633249581 + -7
y = -6.633249581 + -7

Combine like terms: -6.633249581 + -7 = -13.633249581
y = -13.633249581

Simplifying
y = -13.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.366750419, -13.633249581}

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