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 = 54
49 + 14y + y2 = 54

Factor a perfect square on the left side:
(y + 7)(y + 7) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(y + 7) equal to 7.348469228 and -7.348469228.


Subproblem 1
y + 7 = 7.348469228

Simplifying
y + 7 = 7.348469228

Reorder the terms:
7 + y = 7.348469228

Solving
7 + y = 7.348469228

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 = 7.348469228 + -7

Combine like terms: 7 + -7 = 0
0 + y = 7.348469228 + -7
y = 7.348469228 + -7

Combine like terms: 7.348469228 + -7 = 0.348469228
y = 0.348469228

Simplifying
y = 0.348469228


Subproblem 2
y + 7 = -7.348469228

Simplifying
y + 7 = -7.348469228

Reorder the terms:
7 + y = -7.348469228

Solving
7 + y = -7.348469228

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 = -7.348469228 + -7

Combine like terms: 7 + -7 = 0
0 + y = -7.348469228 + -7
y = -7.348469228 + -7

Combine like terms: -7.348469228 + -7 = -14.348469228
y = -14.348469228

Simplifying
y = -14.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.348469228, -14.348469228}

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