-n^2-7n=2

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

Simplifying
-1n2 + -7n = 2

Reorder the terms:
-7n + -1n2 = 2

Solving
-7n + -1n2 = 2

Solving for variable 'n'.

Reorder the terms:
-2 + -7n + -1n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -7n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 7n + n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 7n + n2)' equal to zero and attempt to solve:

Simplifying
2 + 7n + n2 = 0

Solving
2 + 7n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 7n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + 7n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7n + n2 = 0 + -2
7n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
7n + n2 = -2

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = -2 + 12.25

Reorder the terms:
12.25 + 7n + n2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + 7n + n2 = 10.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(n + 3.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
n + 3.5 = 3.201562119

Simplifying
n + 3.5 = 3.201562119

Reorder the terms:
3.5 + n = 3.201562119

Solving
3.5 + n = 3.201562119

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = 3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = 3.201562119 + -3.5
n = 3.201562119 + -3.5

Combine like terms: 3.201562119 + -3.5 = -0.298437881
n = -0.298437881

Simplifying
n = -0.298437881

Subproblem 2
n + 3.5 = -3.201562119

Simplifying
n + 3.5 = -3.201562119

Reorder the terms:
3.5 + n = -3.201562119

Solving
3.5 + n = -3.201562119

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = -3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = -3.201562119 + -3.5
n = -3.201562119 + -3.5

Combine like terms: -3.201562119 + -3.5 = -6.701562119
n = -6.701562119

Simplifying
n = -6.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.298437881, -6.701562119}
Solution
n = {-0.298437881, -6.701562119}