y^2-14y-7=0

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Solution for y^2-14y-7=0 equation: 


Simplifying
y2 + -14y + -7 = 0

Reorder the terms:
-7 + -14y + y2 = 0

Solving
-7 + -14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -14y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + -14y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -14y + y2 = 0 + 7
-14y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
-14y + y2 = 7

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 = 7 + 49

Reorder the terms:
49 + -14y + y2 = 7 + 49

Combine like terms: 7 + 49 = 56
49 + -14y + y2 = 56

Factor a perfect square on the left side:
(y + -7)(y + -7) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(y + -7) equal to 7.483314774 and -7.483314774.


Subproblem 1
y + -7 = 7.483314774

Simplifying
y + -7 = 7.483314774

Reorder the terms:
-7 + y = 7.483314774

Solving
-7 + y = 7.483314774

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 = 7.483314774 + 7

Combine like terms: -7 + 7 = 0
0 + y = 7.483314774 + 7
y = 7.483314774 + 7

Combine like terms: 7.483314774 + 7 = 14.483314774
y = 14.483314774

Simplifying
y = 14.483314774


Subproblem 2
y + -7 = -7.483314774

Simplifying
y + -7 = -7.483314774

Reorder the terms:
-7 + y = -7.483314774

Solving
-7 + y = -7.483314774

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 = -7.483314774 + 7

Combine like terms: -7 + 7 = 0
0 + y = -7.483314774 + 7
y = -7.483314774 + 7

Combine like terms: -7.483314774 + 7 = -0.483314774
y = -0.483314774

Simplifying
y = -0.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.483314774, -0.483314774}

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