n^2+3n+1=0

Simple and best practice solution for n^2+3n+1=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for n^2+3n+1=0 equation:


Simplifying
n2 + 3n + 1 = 0

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

Solving
1 + 3n + n2 = 0

Solving for variable 'n'.

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 = 1.25
2.25 + 3n + n2 = 1.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(n + 1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

n + 1.5 = 1.118033989 Simplifying n + 1.5 = 1.118033989 Reorder the terms: 1.5 + n = 1.118033989 Solving 1.5 + n = 1.118033989 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 = 1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 1.118033989 + -1.5 n = 1.118033989 + -1.5 Combine like terms: 1.118033989 + -1.5 = -0.381966011 n = -0.381966011 Simplifying n = -0.381966011

Subproblem 2

n + 1.5 = -1.118033989 Simplifying n + 1.5 = -1.118033989 Reorder the terms: 1.5 + n = -1.118033989 Solving 1.5 + n = -1.118033989 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 = -1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -1.118033989 + -1.5 n = -1.118033989 + -1.5 Combine like terms: -1.118033989 + -1.5 = -2.618033989 n = -2.618033989 Simplifying n = -2.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.381966011, -2.618033989}

See similar equations:

| 2x+93=180 | | 10-9j=8j | | 3x+3(5x-17)=165 | | -4+4p=-3-1+4p | | 1.5-0.24a=0.09+5.1 | | 90x=11 | | 8x^2+24x=10 | | -7y-9=-10-7y | | (n/9)-(5n/18)=(1-9) | | 2x+2(5x+17)=142 | | d-d=0 | | 0=6f-6f | | 7x=21+10y | | x^4-4x^3+4x^2+3=0 | | (x*40)+[(x*.5)*10]=450 | | -5z=-z-4z | | 3n+n-8=39 | | y=6x^2-12x+10 | | x^4-32x^2=2x+3 | | 10x=12.2222222 | | 7b=6 | | 75+5x-5+4x+2=180 | | -2t=9-t | | -8x+10+9x=3+x+7 | | 0.3(x-5)=0.3x+8-2+0.5 | | 4-2x-3=16 | | 1.5n=1.5 | | -19-14j=6-9j | | ax+y=10 | | -u+5=-17-18u+19u | | -4.4=0.08-0.2r | | (1-i)x-(3-i)=0 |

Equations solver categories