5n^2+2n-7=-5

Solution for 5n^2+2n-7=-5 equation:

Simplifying
5n2 + 2n + -7 = -5

Reorder the terms:
-7 + 2n + 5n2 = -5

Solving
-7 + 2n + 5n2 = -5

Solving for variable 'n'.

Reorder the terms:
-7 + 5 + 2n + 5n2 = -5 + 5

Combine like terms: -7 + 5 = -2
-2 + 2n + 5n2 = -5 + 5

Combine like terms: -5 + 5 = 0
-2 + 2n + 5n2 = 0

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

Divide each side by '5'.
-0.4 + 0.4n + n2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.4n + 0.4 + n2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.4n + n2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.4n + n2 = 0 + 0.4
0.4n + n2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.4n + n2 = 0.4

The n term is 0.4n.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4n + 0.04 + n2 = 0.4 + 0.04

Reorder the terms:
0.04 + 0.4n + n2 = 0.4 + 0.04

Combine like terms: 0.4 + 0.04 = 0.44
0.04 + 0.4n + n2 = 0.44

Factor a perfect square on the left side:
(n + 0.2)(n + 0.2) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(n + 0.2) equal to 0.663324958 and -0.663324958.

Subproblem 1
n + 0.2 = 0.663324958

Simplifying
n + 0.2 = 0.663324958

Reorder the terms:
0.2 + n = 0.663324958

Solving
0.2 + n = 0.663324958

Solving for variable 'n'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + n = 0.663324958 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + n = 0.663324958 + -0.2
n = 0.663324958 + -0.2

Combine like terms: 0.663324958 + -0.2 = 0.463324958
n = 0.463324958

Simplifying
n = 0.463324958

Subproblem 2
n + 0.2 = -0.663324958

Simplifying
n + 0.2 = -0.663324958

Reorder the terms:
0.2 + n = -0.663324958

Solving
0.2 + n = -0.663324958

Solving for variable 'n'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + n = -0.663324958 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + n = -0.663324958 + -0.2
n = -0.663324958 + -0.2

Combine like terms: -0.663324958 + -0.2 = -0.863324958
n = -0.863324958

Simplifying
n = -0.863324958

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.463324958, -0.863324958}