y^2+14y-103=0

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Solution for y^2+14y-103=0 equation: 


Simplifying
y2 + 14y + -103 = 0

Reorder the terms:
-103 + 14y + y2 = 0

Solving
-103 + 14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '103' to each side of the equation.
-103 + 14y + 103 + y2 = 0 + 103

Reorder the terms:
-103 + 103 + 14y + y2 = 0 + 103

Combine like terms: -103 + 103 = 0
0 + 14y + y2 = 0 + 103
14y + y2 = 0 + 103

Combine like terms: 0 + 103 = 103
14y + y2 = 103

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 = 103 + 49

Reorder the terms:
49 + 14y + y2 = 103 + 49

Combine like terms: 103 + 49 = 152
49 + 14y + y2 = 152

Factor a perfect square on the left side:
(y + 7)(y + 7) = 152

Calculate the square root of the right side: 12.328828006

Break this problem into two subproblems by setting 
(y + 7) equal to 12.328828006 and -12.328828006.


Subproblem 1
y + 7 = 12.328828006

Simplifying
y + 7 = 12.328828006

Reorder the terms:
7 + y = 12.328828006

Solving
7 + y = 12.328828006

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 = 12.328828006 + -7

Combine like terms: 7 + -7 = 0
0 + y = 12.328828006 + -7
y = 12.328828006 + -7

Combine like terms: 12.328828006 + -7 = 5.328828006
y = 5.328828006

Simplifying
y = 5.328828006


Subproblem 2
y + 7 = -12.328828006

Simplifying
y + 7 = -12.328828006

Reorder the terms:
7 + y = -12.328828006

Solving
7 + y = -12.328828006

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 = -12.328828006 + -7

Combine like terms: 7 + -7 = 0
0 + y = -12.328828006 + -7
y = -12.328828006 + -7

Combine like terms: -12.328828006 + -7 = -19.328828006
y = -19.328828006

Simplifying
y = -19.328828006


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.328828006, -19.328828006}

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