8n+4n-16=-n^2

Simple and best practice solution for 8n+4n-16=-n^2 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 8n+4n-16=-n^2 equation:


Simplifying
8n + 4n + -16 = -1n2

Reorder the terms:
-16 + 8n + 4n = -1n2

Combine like terms: 8n + 4n = 12n
-16 + 12n = -1n2

Solving
-16 + 12n = -1n2

Solving for variable 'n'.

Combine like terms: -1n2 + n2 = 0
-16 + 12n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 12n + 16 + n2 = 0 + 16

Reorder the terms:
-16 + 16 + 12n + n2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 12n + n2 = 0 + 16
12n + n2 = 0 + 16

Combine like terms: 0 + 16 = 16
12n + n2 = 16

The n term is 12n.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12n + 36 + n2 = 16 + 36

Reorder the terms:
36 + 12n + n2 = 16 + 36

Combine like terms: 16 + 36 = 52
36 + 12n + n2 = 52

Factor a perfect square on the left side:
(n + 6)(n + 6) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(n + 6) equal to 7.211102551 and -7.211102551.

Subproblem 1

n + 6 = 7.211102551 Simplifying n + 6 = 7.211102551 Reorder the terms: 6 + n = 7.211102551 Solving 6 + n = 7.211102551 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = 7.211102551 + -6 Combine like terms: 6 + -6 = 0 0 + n = 7.211102551 + -6 n = 7.211102551 + -6 Combine like terms: 7.211102551 + -6 = 1.211102551 n = 1.211102551 Simplifying n = 1.211102551

Subproblem 2

n + 6 = -7.211102551 Simplifying n + 6 = -7.211102551 Reorder the terms: 6 + n = -7.211102551 Solving 6 + n = -7.211102551 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = -7.211102551 + -6 Combine like terms: 6 + -6 = 0 0 + n = -7.211102551 + -6 n = -7.211102551 + -6 Combine like terms: -7.211102551 + -6 = -13.211102551 n = -13.211102551 Simplifying n = -13.211102551

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.211102551, -13.211102551}

See similar equations:

| 10x+x+5x=180 | | 2x/3=8/6 | | y=18x^2+x-9 | | Y^2-12x=48 | | 6y-19=3y+20 | | x^2-13=24 | | x^4+72x^2-729=0 | | 2y=4y+8 | | 2/11x=18 | | 3ln(2x)=1 | | 0.5x-0.2(30+x)=0.10(30) | | 2m+10m+m=180 | | 21y^4-24y^3/3y^2 | | 8y-1/8(40y-48) | | -12x=35-5x | | 180=6x+(x-2) | | 6x=8x | | 5(x^2+7)=55 | | 3x-5x+8x=5x+18 | | x=24-3x | | -500=(X-5500)0.05 | | x+46/8=-8 | | x(x)+5x(x)=104 | | -2=3x+1/4 | | -900=(6.5-x)3000 | | (5k+5)=(3k+5) | | 5x=2x+6x | | x^4+64x^2-729=0 | | =(6.5-x)3000 | | 5/8x=45 | | 2t+90+10.5t=180 | | 6(x+5)=3(x-14) |

Equations solver categories