5n^2+n+1=0

Simple and best practice solution for 5n^2+n+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 5n^2+n+1=0 equation:


Simplifying
5n2 + n + 1 = 0

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

Solving
1 + n + 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'.
0.2 + 0.2n + n2 = 0

Move the constant term to the right:

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

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

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

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

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2n + 0.25 + n2 = -0.2 + 0.25

Reorder the terms:
0.25 + 0.2n + n2 = -0.2 + 0.25

Combine like terms: -0.2 + 0.25 = 0.05
0.25 + 0.2n + n2 = 0.05

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(n + 0.5) equal to 0.223606798 and -0.223606798.

Subproblem 1

n + 0.5 = 0.223606798 Simplifying n + 0.5 = 0.223606798 Reorder the terms: 0.5 + n = 0.223606798 Solving 0.5 + n = 0.223606798 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 0.223606798 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 0.223606798 + -0.5 n = 0.223606798 + -0.5 Combine like terms: 0.223606798 + -0.5 = -0.276393202 n = -0.276393202 Simplifying n = -0.276393202

Subproblem 2

n + 0.5 = -0.223606798 Simplifying n + 0.5 = -0.223606798 Reorder the terms: 0.5 + n = -0.223606798 Solving 0.5 + n = -0.223606798 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -0.223606798 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -0.223606798 + -0.5 n = -0.223606798 + -0.5 Combine like terms: -0.223606798 + -0.5 = -0.723606798 n = -0.723606798 Simplifying n = -0.723606798

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.276393202, -0.723606798}

See similar equations:

| x=4+-6 | | 2y-2=37-x | | 0.625x-10=0.75x+0.50x | | x^2=39+10x | | 3x^3-x^2-10x=-x^2+2x | | 10n+2=11 | | 4=6-p | | 5*7-y=7+13y | | 5*(7)-y=7+13y | | P^2+4p+4=O | | 5*(7)-y=x+13y | | 6x+(4x-3)=8x+1 | | -3x-1.8=4x+1 | | 22/3.14=(3.14)d/3.14 | | 5*cos^2x-cosx-4=0 | | 5(4y+1)= | | 3r^2-r+4=0 | | 5cos^2x-cosx-4=0 | | 22/3/.14=(3.14)d/3.14 | | 3(2y+2)= | | 0.75x-6=0.125x+4 | | x^2+20=39 | | h(x)=-0.5x^2+4 | | 0.166x+0.083=0.333x-0.166 | | y^2-2y=80 | | 60/x-10logx=33 | | 9.5+8.6x=83.5+x | | 4m^2+m-3=0 | | 9x=62 | | K^2=-8k | | h=16t^2+1600 | | E=280+0.03s |

Equations solver categories