n^2-2n-105=0

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Solution for n^2-2n-105=0 equation: 


Simplifying
n2 + -2n + -105 = 0

Reorder the terms:
-105 + -2n + n2 = 0

Solving
-105 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + -2n + 105 + n2 = 0 + 105

Reorder the terms:
-105 + 105 + -2n + n2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + -2n + n2 = 0 + 105
-2n + n2 = 0 + 105

Combine like terms: 0 + 105 = 105
-2n + n2 = 105

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 105 + 1

Reorder the terms:
1 + -2n + n2 = 105 + 1

Combine like terms: 105 + 1 = 106
1 + -2n + n2 = 106

Factor a perfect square on the left side:
(n + -1)(n + -1) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(n + -1) equal to 10.295630141 and -10.295630141.


Subproblem 1
n + -1 = 10.295630141

Simplifying
n + -1 = 10.295630141

Reorder the terms:
-1 + n = 10.295630141

Solving
-1 + n = 10.295630141

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = 10.295630141 + 1

Combine like terms: -1 + 1 = 0
0 + n = 10.295630141 + 1
n = 10.295630141 + 1

Combine like terms: 10.295630141 + 1 = 11.295630141
n = 11.295630141

Simplifying
n = 11.295630141


Subproblem 2
n + -1 = -10.295630141

Simplifying
n + -1 = -10.295630141

Reorder the terms:
-1 + n = -10.295630141

Solving
-1 + n = -10.295630141

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = -10.295630141 + 1

Combine like terms: -1 + 1 = 0
0 + n = -10.295630141 + 1
n = -10.295630141 + 1

Combine like terms: -10.295630141 + 1 = -9.295630141
n = -9.295630141

Simplifying
n = -9.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {11.295630141, -9.295630141}

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