n(3n-39)=1

Simple and best practice solution for n(3n-39)=1 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(3n-39)=1 equation:


Simplifying
n(3n + -39) = 1

Reorder the terms:
n(-39 + 3n) = 1
(-39 * n + 3n * n) = 1
(-39n + 3n2) = 1

Solving
-39n + 3n2 = 1

Solving for variable 'n'.

Reorder the terms:
-1 + -39n + 3n2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -39n + 3n2 = 0

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

Divide each side by '3'.
-0.3333333333 + -13n + n2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -13n + 0.3333333333 + n2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -13n + n2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -13n + n2 = 0 + 0.3333333333
-13n + n2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-13n + n2 = 0.3333333333

The n term is -13n.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13n + 42.25 + n2 = 0.3333333333 + 42.25

Reorder the terms:
42.25 + -13n + n2 = 0.3333333333 + 42.25

Combine like terms: 0.3333333333 + 42.25 = 42.5833333333
42.25 + -13n + n2 = 42.5833333333

Factor a perfect square on the left side:
(n + -6.5)(n + -6.5) = 42.5833333333

Calculate the square root of the right side: 6.52559065

Break this problem into two subproblems by setting 
(n + -6.5) equal to 6.52559065 and -6.52559065.

Subproblem 1

n + -6.5 = 6.52559065 Simplifying n + -6.5 = 6.52559065 Reorder the terms: -6.5 + n = 6.52559065 Solving -6.5 + n = 6.52559065 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + n = 6.52559065 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = 6.52559065 + 6.5 n = 6.52559065 + 6.5 Combine like terms: 6.52559065 + 6.5 = 13.02559065 n = 13.02559065 Simplifying n = 13.02559065

Subproblem 2

n + -6.5 = -6.52559065 Simplifying n + -6.5 = -6.52559065 Reorder the terms: -6.5 + n = -6.52559065 Solving -6.5 + n = -6.52559065 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + n = -6.52559065 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = -6.52559065 + 6.5 n = -6.52559065 + 6.5 Combine like terms: -6.52559065 + 6.5 = -0.02559065 n = -0.02559065 Simplifying n = -0.02559065

Solution

The solution to the problem is based on the solutions from the subproblems. n = {13.02559065, -0.02559065}

See similar equations:

| 1.66g-5=0.81 | | 3x-4=-5x-3 | | 3n^2-39n-2=0 | | 12x^2-3x^3-5x=9 | | 4x^2-y^2=64 | | 3/14x7/9 | | 7/12=x/30 | | 18+8=26+5x | | S-42=-41 | | 3/x=20/7 | | 3y+2=4y-8 | | X(2-x)=4 | | 3x-14-10x=28 | | -3x+3=-3x-2 | | 8x-7=-49 | | 67323562834582354y-0=0 | | -29.1-s=27.1 | | 3(4x+2)20=20x-9x+2 | | x+9-3=4 | | 4sinx-2cosx/3sinx-2cosx | | 3y+19=(y-2) | | 2=z+6 | | 6-Yb=19 | | 3t-7=5t+15 | | 150x+10000=1300 | | 87n-3n^2=0 | | ln(4x)=2ln(9x) | | -2x-1=-2x-2 | | 87n-3n^2/2 | | -23.6-z=13 | | x*5=x-7 | | 24*371-371*15+371=x |

Equations solver categories