7n^2-14n-22=4

Solution for 7n^2-14n-22=4 equation:

Simplifying
7n2 + -14n + -22 = 4

Reorder the terms:
-22 + -14n + 7n2 = 4

Solving
-22 + -14n + 7n2 = 4

Solving for variable 'n'.

Reorder the terms:
-22 + -4 + -14n + 7n2 = 4 + -4

Combine like terms: -22 + -4 = -26
-26 + -14n + 7n2 = 4 + -4

Combine like terms: 4 + -4 = 0
-26 + -14n + 7n2 = 0

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

Divide each side by '7'.
-3.714285714 + -2n + n2 = 0

Move the constant term to the right:

Add '3.714285714' to each side of the equation.
-3.714285714 + -2n + 3.714285714 + n2 = 0 + 3.714285714

Reorder the terms:
-3.714285714 + 3.714285714 + -2n + n2 = 0 + 3.714285714

Combine like terms: -3.714285714 + 3.714285714 = 0.000000000
0.000000000 + -2n + n2 = 0 + 3.714285714
-2n + n2 = 0 + 3.714285714

Combine like terms: 0 + 3.714285714 = 3.714285714
-2n + n2 = 3.714285714

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 = 3.714285714 + 1

Reorder the terms:
1 + -2n + n2 = 3.714285714 + 1

Combine like terms: 3.714285714 + 1 = 4.714285714
1 + -2n + n2 = 4.714285714

Factor a perfect square on the left side:
(n + -1)(n + -1) = 4.714285714

Calculate the square root of the right side: 2.171240593

Break this problem into two subproblems by setting 
(n + -1) equal to 2.171240593 and -2.171240593.

Subproblem 1
n + -1 = 2.171240593

Simplifying
n + -1 = 2.171240593

Reorder the terms:
-1 + n = 2.171240593

Solving
-1 + n = 2.171240593

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 = 2.171240593 + 1

Combine like terms: -1 + 1 = 0
0 + n = 2.171240593 + 1
n = 2.171240593 + 1

Combine like terms: 2.171240593 + 1 = 3.171240593
n = 3.171240593

Simplifying
n = 3.171240593

Subproblem 2
n + -1 = -2.171240593

Simplifying
n + -1 = -2.171240593

Reorder the terms:
-1 + n = -2.171240593

Solving
-1 + n = -2.171240593

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 = -2.171240593 + 1

Combine like terms: -1 + 1 = 0
0 + n = -2.171240593 + 1
n = -2.171240593 + 1

Combine like terms: -2.171240593 + 1 = -1.171240593
n = -1.171240593

Simplifying
n = -1.171240593

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.171240593, -1.171240593}