n^2+3n+1=2

Solution for n^2+3n+1=2 equation:

Simplifying
n2 + 3n + 1 = 2

Reorder the terms:
1 + 3n + n2 = 2

Solving
1 + 3n + n2 = 2

Solving for variable 'n'.

Reorder the terms:
1 + -2 + 3n + n2 = 2 + -2

Combine like terms: 1 + -2 = -1
-1 + 3n + n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-1 + 3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + 3n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3n + n2 = 0 + 1
3n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
3n + n2 = 1

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 = 1 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + 3n + n2 = 3.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(n + 1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
n + 1.5 = 1.802775638

Simplifying
n + 1.5 = 1.802775638

Reorder the terms:
1.5 + n = 1.802775638

Solving
1.5 + n = 1.802775638

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 = 1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = 1.802775638 + -1.5
n = 1.802775638 + -1.5

Combine like terms: 1.802775638 + -1.5 = 0.302775638
n = 0.302775638

Simplifying
n = 0.302775638

Subproblem 2
n + 1.5 = -1.802775638

Simplifying
n + 1.5 = -1.802775638

Reorder the terms:
1.5 + n = -1.802775638

Solving
1.5 + n = -1.802775638

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 = -1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = -1.802775638 + -1.5
n = -1.802775638 + -1.5

Combine like terms: -1.802775638 + -1.5 = -3.302775638
n = -3.302775638

Simplifying
n = -3.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.302775638, -3.302775638}