7n^2-14n=-1

Solution for 7n^2-14n=-1 equation:

Simplifying
7n2 + -14n = -1

Reorder the terms:
-14n + 7n2 = -1

Solving
-14n + 7n2 = -1

Solving for variable 'n'.

Reorder the terms:
1 + -14n + 7n2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -14n + 7n2 = 0

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

Divide each side by '7'.
0.1428571429 + -2n + n2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -2n + -0.1428571429 + n2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -2n + n2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -2n + n2 = 0 + -0.1428571429
-2n + n2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-2n + n2 = -0.1428571429

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 = -0.1428571429 + 1

Reorder the terms:
1 + -2n + n2 = -0.1428571429 + 1

Combine like terms: -0.1428571429 + 1 = 0.8571428571
1 + -2n + n2 = 0.8571428571

Factor a perfect square on the left side:
(n + -1)(n + -1) = 0.8571428571

Calculate the square root of the right side: 0.9258201

Break this problem into two subproblems by setting 
(n + -1) equal to 0.9258201 and -0.9258201.

Subproblem 1
n + -1 = 0.9258201

Simplifying
n + -1 = 0.9258201

Reorder the terms:
-1 + n = 0.9258201

Solving
-1 + n = 0.9258201

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 = 0.9258201 + 1

Combine like terms: -1 + 1 = 0
0 + n = 0.9258201 + 1
n = 0.9258201 + 1

Combine like terms: 0.9258201 + 1 = 1.9258201
n = 1.9258201

Simplifying
n = 1.9258201

Subproblem 2
n + -1 = -0.9258201

Simplifying
n + -1 = -0.9258201

Reorder the terms:
-1 + n = -0.9258201

Solving
-1 + n = -0.9258201

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 = -0.9258201 + 1

Combine like terms: -1 + 1 = 0
0 + n = -0.9258201 + 1
n = -0.9258201 + 1

Combine like terms: -0.9258201 + 1 = 0.0741799
n = 0.0741799

Simplifying
n = 0.0741799

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.9258201, 0.0741799}