y^2+14y+27=0

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Solution for y^2+14y+27=0 equation: 


Simplifying
y2 + 14y + 27 = 0

Reorder the terms:
27 + 14y + y2 = 0

Solving
27 + 14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 14y + -27 + y2 = 0 + -27

Reorder the terms:
27 + -27 + 14y + y2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 14y + y2 = 0 + -27
14y + y2 = 0 + -27

Combine like terms: 0 + -27 = -27
14y + y2 = -27

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 = -27 + 49

Reorder the terms:
49 + 14y + y2 = -27 + 49

Combine like terms: -27 + 49 = 22
49 + 14y + y2 = 22

Factor a perfect square on the left side:
(y + 7)(y + 7) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(y + 7) equal to 4.69041576 and -4.69041576.


Subproblem 1
y + 7 = 4.69041576

Simplifying
y + 7 = 4.69041576

Reorder the terms:
7 + y = 4.69041576

Solving
7 + y = 4.69041576

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 = 4.69041576 + -7

Combine like terms: 7 + -7 = 0
0 + y = 4.69041576 + -7
y = 4.69041576 + -7

Combine like terms: 4.69041576 + -7 = -2.30958424
y = -2.30958424

Simplifying
y = -2.30958424


Subproblem 2
y + 7 = -4.69041576

Simplifying
y + 7 = -4.69041576

Reorder the terms:
7 + y = -4.69041576

Solving
7 + y = -4.69041576

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 = -4.69041576 + -7

Combine like terms: 7 + -7 = 0
0 + y = -4.69041576 + -7
y = -4.69041576 + -7

Combine like terms: -4.69041576 + -7 = -11.69041576
y = -11.69041576

Simplifying
y = -11.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.30958424, -11.69041576}

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