n^2-5n+5.76=0

Solution for n^2-5n+5.76=0 equation:

Simplifying
n2 + -5n + 5.76 = 0

Reorder the terms:
5.76 + -5n + n2 = 0

Solving
5.76 + -5n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-5.76' to each side of the equation.
5.76 + -5n + -5.76 + n2 = 0 + -5.76

Reorder the terms:
5.76 + -5.76 + -5n + n2 = 0 + -5.76

Combine like terms: 5.76 + -5.76 = 0.00
0.00 + -5n + n2 = 0 + -5.76
-5n + n2 = 0 + -5.76

Combine like terms: 0 + -5.76 = -5.76
-5n + n2 = -5.76

The n term is -5n.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5n + 6.25 + n2 = -5.76 + 6.25

Reorder the terms:
6.25 + -5n + n2 = -5.76 + 6.25

Combine like terms: -5.76 + 6.25 = 0.49
6.25 + -5n + n2 = 0.49

Factor a perfect square on the left side:
(n + -2.5)(n + -2.5) = 0.49

Calculate the square root of the right side: 0.7

Break this problem into two subproblems by setting 
(n + -2.5) equal to 0.7 and -0.7.

Subproblem 1
n + -2.5 = 0.7

Simplifying
n + -2.5 = 0.7

Reorder the terms:
-2.5 + n = 0.7

Solving
-2.5 + n = 0.7

Solving for variable 'n'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + n = 0.7 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = 0.7 + 2.5
n = 0.7 + 2.5

Combine like terms: 0.7 + 2.5 = 3.2
n = 3.2

Simplifying
n = 3.2

Subproblem 2
n + -2.5 = -0.7

Simplifying
n + -2.5 = -0.7

Reorder the terms:
-2.5 + n = -0.7

Solving
-2.5 + n = -0.7

Solving for variable 'n'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + n = -0.7 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = -0.7 + 2.5
n = -0.7 + 2.5

Combine like terms: -0.7 + 2.5 = 1.8
n = 1.8

Simplifying
n = 1.8

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.2, 1.8}