2n^2+7n+1=0

Solution for 2n^2+7n+1=0 equation:

Simplifying
2n2 + 7n + 1 = 0

Reorder the terms:
1 + 7n + 2n2 = 0

Solving
1 + 7n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
0.5 + 3.5n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 3.5n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 3.5n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 3.5n + n2 = 0 + -0.5
3.5n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
3.5n + n2 = -0.5

The n term is 3.5n.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5n + 3.0625 + n2 = -0.5 + 3.0625

Reorder the terms:
3.0625 + 3.5n + n2 = -0.5 + 3.0625

Combine like terms: -0.5 + 3.0625 = 2.5625
3.0625 + 3.5n + n2 = 2.5625

Factor a perfect square on the left side:
(n + 1.75)(n + 1.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(n + 1.75) equal to 1.600781059 and -1.600781059.

Subproblem 1
n + 1.75 = 1.600781059

Simplifying
n + 1.75 = 1.600781059

Reorder the terms:
1.75 + n = 1.600781059

Solving
1.75 + n = 1.600781059

Solving for variable 'n'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + n = 1.600781059 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + n = 1.600781059 + -1.75
n = 1.600781059 + -1.75

Combine like terms: 1.600781059 + -1.75 = -0.149218941
n = -0.149218941

Simplifying
n = -0.149218941

Subproblem 2
n + 1.75 = -1.600781059

Simplifying
n + 1.75 = -1.600781059

Reorder the terms:
1.75 + n = -1.600781059

Solving
1.75 + n = -1.600781059

Solving for variable 'n'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + n = -1.600781059 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + n = -1.600781059 + -1.75
n = -1.600781059 + -1.75

Combine like terms: -1.600781059 + -1.75 = -3.350781059
n = -3.350781059

Simplifying
n = -3.350781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.149218941, -3.350781059}