14n^2+27n+2=

Solution for 14n^2+27n+2= equation:

Simplifying
14n2 + 27n + 2 = 0

Reorder the terms:
2 + 27n + 14n2 = 0

Solving
2 + 27n + 14n2 = 0

Solving for variable 'n'.

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

Divide each side by '14'.
0.1428571429 + 1.928571429n + n2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + 1.928571429n + -0.1428571429 + n2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + 1.928571429n + n2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + 1.928571429n + n2 = 0 + -0.1428571429
1.928571429n + n2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
1.928571429n + n2 = -0.1428571429

The n term is 1.928571429n.  Take half its coefficient (0.9642857145).
Square it (0.9298469392) and add it to both sides.

Add '0.9298469392' to each side of the equation.
1.928571429n + 0.9298469392 + n2 = -0.1428571429 + 0.9298469392

Reorder the terms:
0.9298469392 + 1.928571429n + n2 = -0.1428571429 + 0.9298469392

Combine like terms: -0.1428571429 + 0.9298469392 = 0.7869897963
0.9298469392 + 1.928571429n + n2 = 0.7869897963

Factor a perfect square on the left side:
(n + 0.9642857145)(n + 0.9642857145) = 0.7869897963

Calculate the square root of the right side: 0.887124454

Break this problem into two subproblems by setting 
(n + 0.9642857145) equal to 0.887124454 and -0.887124454.

Subproblem 1
n + 0.9642857145 = 0.887124454

Simplifying
n + 0.9642857145 = 0.887124454

Reorder the terms:
0.9642857145 + n = 0.887124454

Solving
0.9642857145 + n = 0.887124454

Solving for variable 'n'.

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

Add '-0.9642857145' to each side of the equation.
0.9642857145 + -0.9642857145 + n = 0.887124454 + -0.9642857145

Combine like terms: 0.9642857145 + -0.9642857145 = 0.0000000000
0.0000000000 + n = 0.887124454 + -0.9642857145
n = 0.887124454 + -0.9642857145

Combine like terms: 0.887124454 + -0.9642857145 = -0.0771612605
n = -0.0771612605

Simplifying
n = -0.0771612605

Subproblem 2
n + 0.9642857145 = -0.887124454

Simplifying
n + 0.9642857145 = -0.887124454

Reorder the terms:
0.9642857145 + n = -0.887124454

Solving
0.9642857145 + n = -0.887124454

Solving for variable 'n'.

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

Add '-0.9642857145' to each side of the equation.
0.9642857145 + -0.9642857145 + n = -0.887124454 + -0.9642857145

Combine like terms: 0.9642857145 + -0.9642857145 = 0.0000000000
0.0000000000 + n = -0.887124454 + -0.9642857145
n = -0.887124454 + -0.9642857145

Combine like terms: -0.887124454 + -0.9642857145 = -1.8514101685
n = -1.8514101685

Simplifying
n = -1.8514101685

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.0771612605, -1.8514101685}