7n^2-14n-101=-5

Solution for 7n^2-14n-101=-5 equation:

Simplifying
7n2 + -14n + -101 = -5

Reorder the terms:
-101 + -14n + 7n2 = -5

Solving
-101 + -14n + 7n2 = -5

Solving for variable 'n'.

Reorder the terms:
-101 + 5 + -14n + 7n2 = -5 + 5

Combine like terms: -101 + 5 = -96
-96 + -14n + 7n2 = -5 + 5

Combine like terms: -5 + 5 = 0
-96 + -14n + 7n2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-13.71428571 + -2n + n2 = 0

Move the constant term to the right:

Add '13.71428571' to each side of the equation.
-13.71428571 + -2n + 13.71428571 + n2 = 0 + 13.71428571

Reorder the terms:
-13.71428571 + 13.71428571 + -2n + n2 = 0 + 13.71428571

Combine like terms: -13.71428571 + 13.71428571 = 0.00000000
0.00000000 + -2n + n2 = 0 + 13.71428571
-2n + n2 = 0 + 13.71428571

Combine like terms: 0 + 13.71428571 = 13.71428571
-2n + n2 = 13.71428571

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 = 13.71428571 + 1

Reorder the terms:
1 + -2n + n2 = 13.71428571 + 1

Combine like terms: 13.71428571 + 1 = 14.71428571
1 + -2n + n2 = 14.71428571

Factor a perfect square on the left side:
(n + -1)(n + -1) = 14.71428571

Calculate the square root of the right side: 3.835920451

Break this problem into two subproblems by setting 
(n + -1) equal to 3.835920451 and -3.835920451.

Subproblem 1
n + -1 = 3.835920451

Simplifying
n + -1 = 3.835920451

Reorder the terms:
-1 + n = 3.835920451

Solving
-1 + n = 3.835920451

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 = 3.835920451 + 1

Combine like terms: -1 + 1 = 0
0 + n = 3.835920451 + 1
n = 3.835920451 + 1

Combine like terms: 3.835920451 + 1 = 4.835920451
n = 4.835920451

Simplifying
n = 4.835920451

Subproblem 2
n + -1 = -3.835920451

Simplifying
n + -1 = -3.835920451

Reorder the terms:
-1 + n = -3.835920451

Solving
-1 + n = -3.835920451

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 = -3.835920451 + 1

Combine like terms: -1 + 1 = 0
0 + n = -3.835920451 + 1
n = -3.835920451 + 1

Combine like terms: -3.835920451 + 1 = -2.835920451
n = -2.835920451

Simplifying
n = -2.835920451

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.835920451, -2.835920451}