5n^2-1n-26=0

Solution for 5n^2-1n-26=0 equation:

Simplifying
5n2 + -1n + -26 = 0

Reorder the terms:
-26 + -1n + 5n2 = 0

Solving
-26 + -1n + 5n2 = 0

Solving for variable 'n'.

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

Divide each side by '5'.
-5.2 + -0.2n + n2 = 0

Move the constant term to the right:

Add '5.2' to each side of the equation.
-5.2 + -0.2n + 5.2 + n2 = 0 + 5.2

Reorder the terms:
-5.2 + 5.2 + -0.2n + n2 = 0 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + -0.2n + n2 = 0 + 5.2
-0.2n + n2 = 0 + 5.2

Combine like terms: 0 + 5.2 = 5.2
-0.2n + n2 = 5.2

The n term is -0.2n.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2n + 0.01 + n2 = 5.2 + 0.01

Reorder the terms:
0.01 + -0.2n + n2 = 5.2 + 0.01

Combine like terms: 5.2 + 0.01 = 5.21
0.01 + -0.2n + n2 = 5.21

Factor a perfect square on the left side:
(n + -0.1)(n + -0.1) = 5.21

Calculate the square root of the right side: 2.282542442

Break this problem into two subproblems by setting 
(n + -0.1) equal to 2.282542442 and -2.282542442.

Subproblem 1
n + -0.1 = 2.282542442

Simplifying
n + -0.1 = 2.282542442

Reorder the terms:
-0.1 + n = 2.282542442

Solving
-0.1 + n = 2.282542442

Solving for variable 'n'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + n = 2.282542442 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + n = 2.282542442 + 0.1
n = 2.282542442 + 0.1

Combine like terms: 2.282542442 + 0.1 = 2.382542442
n = 2.382542442

Simplifying
n = 2.382542442

Subproblem 2
n + -0.1 = -2.282542442

Simplifying
n + -0.1 = -2.282542442

Reorder the terms:
-0.1 + n = -2.282542442

Solving
-0.1 + n = -2.282542442

Solving for variable 'n'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + n = -2.282542442 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + n = -2.282542442 + 0.1
n = -2.282542442 + 0.1

Combine like terms: -2.282542442 + 0.1 = -2.182542442
n = -2.182542442

Simplifying
n = -2.182542442

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.382542442, -2.182542442}