n(n-13)=50

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Solution for n(n-13)=50 equation: 


Simplifying
n(n + -13) = 50

Reorder the terms:
n(-13 + n) = 50
(-13 * n + n * n) = 50
(-13n + n2) = 50

Solving
-13n + n2 = 50

Solving for variable 'n'.

Reorder the terms:
-50 + -13n + n2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + -13n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -13n + 50 + n2 = 0 + 50

Reorder the terms:
-50 + 50 + -13n + n2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -13n + n2 = 0 + 50
-13n + n2 = 0 + 50

Combine like terms: 0 + 50 = 50
-13n + n2 = 50

The n term is -13n.  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.
-13n + 42.25 + n2 = 50 + 42.25

Reorder the terms:
42.25 + -13n + n2 = 50 + 42.25

Combine like terms: 50 + 42.25 = 92.25
42.25 + -13n + n2 = 92.25

Factor a perfect square on the left side:
(n + -6.5)(n + -6.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(n + -6.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
n + -6.5 = 9.604686356

Simplifying
n + -6.5 = 9.604686356

Reorder the terms:
-6.5 + n = 9.604686356

Solving
-6.5 + n = 9.604686356

Solving for variable 'n'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + n = 9.604686356 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + n = 9.604686356 + 6.5
n = 9.604686356 + 6.5

Combine like terms: 9.604686356 + 6.5 = 16.104686356
n = 16.104686356

Simplifying
n = 16.104686356


Subproblem 2
n + -6.5 = -9.604686356

Simplifying
n + -6.5 = -9.604686356

Reorder the terms:
-6.5 + n = -9.604686356

Solving
-6.5 + n = -9.604686356

Solving for variable 'n'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + n = -9.604686356 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + n = -9.604686356 + 6.5
n = -9.604686356 + 6.5

Combine like terms: -9.604686356 + 6.5 = -3.104686356
n = -3.104686356

Simplifying
n = -3.104686356


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {16.104686356, -3.104686356}

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