N^2+12N+10=4

Solution for N^2+12N+10=4 equation:

Simplifying
N2 + 12N + 10 = 4

Reorder the terms:
10 + 12N + N2 = 4

Solving
10 + 12N + N2 = 4

Solving for variable 'N'.

Reorder the terms:
10 + -4 + 12N + N2 = 4 + -4

Combine like terms: 10 + -4 = 6
6 + 12N + N2 = 4 + -4

Combine like terms: 4 + -4 = 0
6 + 12N + N2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 12N + -6 + N2 = 0 + -6

Reorder the terms:
6 + -6 + 12N + N2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 12N + N2 = 0 + -6
12N + N2 = 0 + -6

Combine like terms: 0 + -6 = -6
12N + N2 = -6

The N term is 12N.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12N + 36 + N2 = -6 + 36

Reorder the terms:
36 + 12N + N2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + 12N + N2 = 30

Factor a perfect square on the left side:
(N + 6)(N + 6) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(N + 6) equal to 5.477225575 and -5.477225575.

Subproblem 1
N + 6 = 5.477225575

Simplifying
N + 6 = 5.477225575

Reorder the terms:
6 + N = 5.477225575

Solving
6 + N = 5.477225575

Solving for variable 'N'.

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

Add '-6' to each side of the equation.
6 + -6 + N = 5.477225575 + -6

Combine like terms: 6 + -6 = 0
0 + N = 5.477225575 + -6
N = 5.477225575 + -6

Combine like terms: 5.477225575 + -6 = -0.522774425
N = -0.522774425

Simplifying
N = -0.522774425

Subproblem 2
N + 6 = -5.477225575

Simplifying
N + 6 = -5.477225575

Reorder the terms:
6 + N = -5.477225575

Solving
6 + N = -5.477225575

Solving for variable 'N'.

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

Add '-6' to each side of the equation.
6 + -6 + N = -5.477225575 + -6

Combine like terms: 6 + -6 = 0
0 + N = -5.477225575 + -6
N = -5.477225575 + -6

Combine like terms: -5.477225575 + -6 = -11.477225575
N = -11.477225575

Simplifying
N = -11.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {-0.522774425, -11.477225575}