(n^2)+6n=3+n

Simple and best practice solution for (n^2)+6n=3+n 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)+6n=3+n equation:


Simplifying
(n2) + 6n = 3 + n
n2 + 6n = 3 + n

Reorder the terms:
6n + n2 = 3 + n

Solving
6n + n2 = 3 + n

Solving for variable 'n'.

Reorder the terms:
-3 + 6n + -1n + n2 = 3 + n + -3 + -1n

Combine like terms: 6n + -1n = 5n
-3 + 5n + n2 = 3 + n + -3 + -1n

Reorder the terms:
-3 + 5n + n2 = 3 + -3 + n + -1n

Combine like terms: 3 + -3 = 0
-3 + 5n + n2 = 0 + n + -1n
-3 + 5n + n2 = n + -1n

Combine like terms: n + -1n = 0
-3 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 5n + 3 + n2 = 0 + 3

Reorder the terms:
-3 + 3 + 5n + n2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5n + n2 = 0 + 3
5n + n2 = 0 + 3

Combine like terms: 0 + 3 = 3
5n + n2 = 3

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = 3 + 6.25

Reorder the terms:
6.25 + 5n + n2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + 5n + n2 = 9.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(n + 2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

n + 2.5 = 3.041381265 Simplifying n + 2.5 = 3.041381265 Reorder the terms: 2.5 + n = 3.041381265 Solving 2.5 + n = 3.041381265 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 3.041381265 + -2.5 n = 3.041381265 + -2.5 Combine like terms: 3.041381265 + -2.5 = 0.541381265 n = 0.541381265 Simplifying n = 0.541381265

Subproblem 2

n + 2.5 = -3.041381265 Simplifying n + 2.5 = -3.041381265 Reorder the terms: 2.5 + n = -3.041381265 Solving 2.5 + n = -3.041381265 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -3.041381265 + -2.5 n = -3.041381265 + -2.5 Combine like terms: -3.041381265 + -2.5 = -5.541381265 n = -5.541381265 Simplifying n = -5.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.541381265, -5.541381265}

See similar equations:

| 2x^2+16=16 | | 8x+8=-6 | | (4v^2)-(20v)=0 | | a-2b+6c-6x=6 | | 3r-2(r+3)+2r=6r-6-3r+10 | | 4.3+1.7x=41.94 | | 7x+1=2y | | 13(4c-1)-16=50c+13 | | a-2(b-3c+3x)=6 | | -x+73=-62+8x | | 9x^2+18x-4=2-7x | | 5x-2=5(X-7) | | 8.25+0.25x=10.75 | | 0.04(3t-7)=0.12(t+3)-0.64 | | 4(5x+8)=-25+17 | | X+x-31+x+42=180 | | 7x-1-5x-3=2 | | 8x+9=9x+1 | | -2u^2-15u+8=0 | | 12x-9=-5 | | 0.05-0.03(x+2)=-0.04(2-x) | | 11x=10(1-y) | | 4+2n=16 | | -x+6y=-37 | | 1+2x/5+3-x/2=9/10 | | 12=-7f-5 | | 5z^2-75z+70= | | 3(3x+4)=7(x+4)-10 | | 104=-6x-4(2x+16) | | 2n^2+4n=5 | | 25x^2+15x+1=0 | | (x+1)(x+2)-3=0 |

Equations solver categories