y^2-13y-7=0

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Solution for y^2-13y-7=0 equation: 


Simplifying
y2 + -13y + -7 = 0

Reorder the terms:
-7 + -13y + y2 = 0

Solving
-7 + -13y + 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 + -13y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + -13y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13y + y2 = 0 + 7
-13y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
-13y + y2 = 7

The y term is -13y.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13y + 42.25 + y2 = 7 + 42.25

Reorder the terms:
42.25 + -13y + y2 = 7 + 42.25

Combine like terms: 7 + 42.25 = 49.25
42.25 + -13y + y2 = 49.25

Factor a perfect square on the left side:
(y + -6.5)(y + -6.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(y + -6.5) equal to 7.017834424 and -7.017834424.


Subproblem 1
y + -6.5 = 7.017834424

Simplifying
y + -6.5 = 7.017834424

Reorder the terms:
-6.5 + y = 7.017834424

Solving
-6.5 + y = 7.017834424

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + y = 7.017834424 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = 7.017834424 + 6.5
y = 7.017834424 + 6.5

Combine like terms: 7.017834424 + 6.5 = 13.517834424
y = 13.517834424

Simplifying
y = 13.517834424


Subproblem 2
y + -6.5 = -7.017834424

Simplifying
y + -6.5 = -7.017834424

Reorder the terms:
-6.5 + y = -7.017834424

Solving
-6.5 + y = -7.017834424

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + y = -7.017834424 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = -7.017834424 + 6.5
y = -7.017834424 + 6.5

Combine like terms: -7.017834424 + 6.5 = -0.517834424
y = -0.517834424

Simplifying
y = -0.517834424


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {13.517834424, -0.517834424}

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