n^2-8n=15

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Solution for n^2-8n=15 equation: 


Simplifying
n2 + -8n = 15

Reorder the terms:
-8n + n2 = 15

Solving
-8n + n2 = 15

Solving for variable 'n'.

Reorder the terms:
-15 + -8n + n2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -8n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -8n + 15 + n2 = 0 + 15

Reorder the terms:
-15 + 15 + -8n + n2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -8n + n2 = 0 + 15
-8n + n2 = 0 + 15

Combine like terms: 0 + 15 = 15
-8n + n2 = 15

The n term is -8n.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n + 16 + n2 = 15 + 16

Reorder the terms:
16 + -8n + n2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + -8n + n2 = 31

Factor a perfect square on the left side:
(n + -4)(n + -4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(n + -4) equal to 5.567764363 and -5.567764363.


Subproblem 1
n + -4 = 5.567764363

Simplifying
n + -4 = 5.567764363

Reorder the terms:
-4 + n = 5.567764363

Solving
-4 + n = 5.567764363

Solving for variable 'n'.

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

Add '4' to each side of the equation.
-4 + 4 + n = 5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + n = 5.567764363 + 4
n = 5.567764363 + 4

Combine like terms: 5.567764363 + 4 = 9.567764363
n = 9.567764363

Simplifying
n = 9.567764363


Subproblem 2
n + -4 = -5.567764363

Simplifying
n + -4 = -5.567764363

Reorder the terms:
-4 + n = -5.567764363

Solving
-4 + n = -5.567764363

Solving for variable 'n'.

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

Add '4' to each side of the equation.
-4 + 4 + n = -5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + n = -5.567764363 + 4
n = -5.567764363 + 4

Combine like terms: -5.567764363 + 4 = -1.567764363
n = -1.567764363

Simplifying
n = -1.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.567764363, -1.567764363}

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