y^2-14y-13=0

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Solution for y^2-14y-13=0 equation: 


Simplifying
y2 + -14y + -13 = 0

Reorder the terms:
-13 + -14y + y2 = 0

Solving
-13 + -14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -14y + 13 + y2 = 0 + 13

Reorder the terms:
-13 + 13 + -14y + y2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -14y + y2 = 0 + 13
-14y + y2 = 0 + 13

Combine like terms: 0 + 13 = 13
-14y + y2 = 13

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 = 13 + 49

Reorder the terms:
49 + -14y + y2 = 13 + 49

Combine like terms: 13 + 49 = 62
49 + -14y + y2 = 62

Factor a perfect square on the left side:
(y + -7)(y + -7) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(y + -7) equal to 7.874007874 and -7.874007874.


Subproblem 1
y + -7 = 7.874007874

Simplifying
y + -7 = 7.874007874

Reorder the terms:
-7 + y = 7.874007874

Solving
-7 + y = 7.874007874

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 = 7.874007874 + 7

Combine like terms: -7 + 7 = 0
0 + y = 7.874007874 + 7
y = 7.874007874 + 7

Combine like terms: 7.874007874 + 7 = 14.874007874
y = 14.874007874

Simplifying
y = 14.874007874


Subproblem 2
y + -7 = -7.874007874

Simplifying
y + -7 = -7.874007874

Reorder the terms:
-7 + y = -7.874007874

Solving
-7 + y = -7.874007874

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 = -7.874007874 + 7

Combine like terms: -7 + 7 = 0
0 + y = -7.874007874 + 7
y = -7.874007874 + 7

Combine like terms: -7.874007874 + 7 = -0.874007874
y = -0.874007874

Simplifying
y = -0.874007874


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.874007874, -0.874007874}

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