0=9n^2-3n-968

Simple and best practice solution for 0=9n^2-3n-968 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 0=9n^2-3n-968 equation:


Simplifying
0 = 9n2 + -3n + -968

Reorder the terms:
0 = -968 + -3n + 9n2

Solving
0 = -968 + -3n + 9n2

Solving for variable 'n'.

Combine like terms: 0 + 968 = 968
968 + 3n + -9n2 = -968 + -3n + 9n2 + 968 + 3n + -9n2

Reorder the terms:
968 + 3n + -9n2 = -968 + 968 + -3n + 3n + 9n2 + -9n2

Combine like terms: -968 + 968 = 0
968 + 3n + -9n2 = 0 + -3n + 3n + 9n2 + -9n2
968 + 3n + -9n2 = -3n + 3n + 9n2 + -9n2

Combine like terms: -3n + 3n = 0
968 + 3n + -9n2 = 0 + 9n2 + -9n2
968 + 3n + -9n2 = 9n2 + -9n2

Combine like terms: 9n2 + -9n2 = 0
968 + 3n + -9n2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-107.5555556 + -0.3333333333n + n2 = 0

Move the constant term to the right:

Add '107.5555556' to each side of the equation.
-107.5555556 + -0.3333333333n + 107.5555556 + n2 = 0 + 107.5555556

Reorder the terms:
-107.5555556 + 107.5555556 + -0.3333333333n + n2 = 0 + 107.5555556

Combine like terms: -107.5555556 + 107.5555556 = 0.0000000
0.0000000 + -0.3333333333n + n2 = 0 + 107.5555556
-0.3333333333n + n2 = 0 + 107.5555556

Combine like terms: 0 + 107.5555556 = 107.5555556
-0.3333333333n + n2 = 107.5555556

The n term is -0.3333333333n.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333n + 0.02777777779 + n2 = 107.5555556 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333n + n2 = 107.5555556 + 0.02777777779

Combine like terms: 107.5555556 + 0.02777777779 = 107.58333337779
0.02777777779 + -0.3333333333n + n2 = 107.58333337779

Factor a perfect square on the left side:
(n + -0.1666666667)(n + -0.1666666667) = 107.58333337779

Calculate the square root of the right side: 10.37223859

Break this problem into two subproblems by setting 
(n + -0.1666666667) equal to 10.37223859 and -10.37223859.

Subproblem 1

n + -0.1666666667 = 10.37223859 Simplifying n + -0.1666666667 = 10.37223859 Reorder the terms: -0.1666666667 + n = 10.37223859 Solving -0.1666666667 + n = 10.37223859 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + n = 10.37223859 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + n = 10.37223859 + 0.1666666667 n = 10.37223859 + 0.1666666667 Combine like terms: 10.37223859 + 0.1666666667 = 10.5389052567 n = 10.5389052567 Simplifying n = 10.5389052567

Subproblem 2

n + -0.1666666667 = -10.37223859 Simplifying n + -0.1666666667 = -10.37223859 Reorder the terms: -0.1666666667 + n = -10.37223859 Solving -0.1666666667 + n = -10.37223859 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + n = -10.37223859 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + n = -10.37223859 + 0.1666666667 n = -10.37223859 + 0.1666666667 Combine like terms: -10.37223859 + 0.1666666667 = -10.2055719233 n = -10.2055719233 Simplifying n = -10.2055719233

Solution

The solution to the problem is based on the solutions from the subproblems. n = {10.5389052567, -10.2055719233}

See similar equations:

| 8.3=0.75x-.6 | | (3x-3)(x-1)+5=32 | | -2-w=4sr+9 | | 87=14x | | .625p=2.25-.378 | | 1.75+2x=-3.25 | | 6+7x=4x+21 | | 1.4y=3-0.2 | | 5=-3x+27 | | .6x-5=1 | | 4(6a-7)=8(4a+2) | | 13x+9=100 | | 2(10.26)+x=20 | | 7(p+2)=7(2+8p) | | 5+0.09m=15.08 | | 6(12+2x)=4(2x-2) | | 2(2x-5)-3(4-6x)=6 | | 77n=105 | | 2343=86 | | 20.95+0.85m=139.10 | | 4A-3A+28A+70=78 | | 24a-28=32a+16 | | -63.376=7.2(9c+1) | | 0.5x+55=55 | | 30-9=15 | | 70=36.65+7.25p | | 7(3x+4)-6= | | 3(4w+4)=4 | | 2y^2+4y+30=(Y-3)(y-3) | | -1x+2x=-3+24x | | -5(2t+3)=5 | | 2(f-4)=4 |

Equations solver categories