n*n=3n+2.8

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Solution for n*n=3n+2.8 equation: 


Simplifying
n * n = 3n + 2.8

Multiply n * n
n2 = 3n + 2.8

Reorder the terms:
n2 = 2.8 + 3n

Solving
n2 = 2.8 + 3n

Solving for variable 'n'.

Reorder the terms:
-2.8 + -3n + n2 = 2.8 + 3n + -2.8 + -3n

Reorder the terms:
-2.8 + -3n + n2 = 2.8 + -2.8 + 3n + -3n

Combine like terms: 2.8 + -2.8 = 0.0
-2.8 + -3n + n2 = 0.0 + 3n + -3n
-2.8 + -3n + n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-2.8 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -3n + 2.8 + n2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -3n + n2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -3n + n2 = 0 + 2.8
-3n + n2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-3n + n2 = 2.8

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 2.8 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 2.8 + 2.25

Combine like terms: 2.8 + 2.25 = 5.05
2.25 + -3n + n2 = 5.05

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 5.05

Calculate the square root of the right side: 2.247220505

Break this problem into two subproblems by setting 
(n + -1.5) equal to 2.247220505 and -2.247220505.


Subproblem 1
n + -1.5 = 2.247220505

Simplifying
n + -1.5 = 2.247220505

Reorder the terms:
-1.5 + n = 2.247220505

Solving
-1.5 + n = 2.247220505

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 2.247220505 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 2.247220505 + 1.5
n = 2.247220505 + 1.5

Combine like terms: 2.247220505 + 1.5 = 3.747220505
n = 3.747220505

Simplifying
n = 3.747220505


Subproblem 2
n + -1.5 = -2.247220505

Simplifying
n + -1.5 = -2.247220505

Reorder the terms:
-1.5 + n = -2.247220505

Solving
-1.5 + n = -2.247220505

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -2.247220505 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -2.247220505 + 1.5
n = -2.247220505 + 1.5

Combine like terms: -2.247220505 + 1.5 = -0.747220505
n = -0.747220505

Simplifying
n = -0.747220505


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.747220505, -0.747220505}

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