5n^2+5n+1=0

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


Simplifying
5n2 + 5n + 1 = 0

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

Solving
1 + 5n + 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 + n + n2 = 0

Move the constant term to the right:

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

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

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

Combine like terms: 0 + -0.2 = -0.2
n + 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.
 + 0.25 + n2 = -0.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = -0.2 + 0.25

Combine like terms: -0.2 + 0.25 = 0.05
1.25 + 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:

| (8x+3)2=16 | | -x-4/5=x+1/4+1/5 | | 180-(4n-6)=x | | x+b+(5x+12)=180 | | 2(y-5)/3=-4y | | (4n-6)+(4n-6)=90 | | 180-138=x | | 10w-20=-110 | | 3y-6=-30 | | 180-24=x | | m^2+3m-54= | | (4n-6)=90 | | 1/2=5x/10 | | (4n-6)=(4n-6) | | 8(x-3)=6x+7-5x | | 0.12(y-6)+0.10y=0.16-0.03(10) | | 5y-8-y=b | | b^2-8b+16=7 | | 1c+9c+20=0 | | 180(5x+15)=b | | 5g-10=-45 | | 1y-4y+3=0 | | 17y-26=76 | | 8v-16=64 | | 8x-9=-33 | | 6.75-y=0 | | 3x=18-7x | | 10q=-219 | | 4/3+8y/3-3/6=4+7/2 | | r^2+12r+36= | | 1r+3r-10=0 | | w+25=10 |

Equations solver categories