y^2-13y-16=0

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Solution for y^2-13y-16=0 equation: 


Simplifying
y2 + -13y + -16 = 0

Reorder the terms:
-16 + -13y + y2 = 0

Solving
-16 + -13y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -13y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + -13y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -13y + y2 = 0 + 16
-13y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
-13y + y2 = 16

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 = 16 + 42.25

Reorder the terms:
42.25 + -13y + y2 = 16 + 42.25

Combine like terms: 16 + 42.25 = 58.25
42.25 + -13y + y2 = 58.25

Factor a perfect square on the left side:
(y + -6.5)(y + -6.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(y + -6.5) equal to 7.632168761 and -7.632168761.


Subproblem 1
y + -6.5 = 7.632168761

Simplifying
y + -6.5 = 7.632168761

Reorder the terms:
-6.5 + y = 7.632168761

Solving
-6.5 + y = 7.632168761

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 = 7.632168761 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = 7.632168761 + 6.5
y = 7.632168761 + 6.5

Combine like terms: 7.632168761 + 6.5 = 14.132168761
y = 14.132168761

Simplifying
y = 14.132168761


Subproblem 2
y + -6.5 = -7.632168761

Simplifying
y + -6.5 = -7.632168761

Reorder the terms:
-6.5 + y = -7.632168761

Solving
-6.5 + y = -7.632168761

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 = -7.632168761 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = -7.632168761 + 6.5
y = -7.632168761 + 6.5

Combine like terms: -7.632168761 + 6.5 = -1.132168761
y = -1.132168761

Simplifying
y = -1.132168761


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.132168761, -1.132168761}

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