n(n-3)=65

Simple and best practice solution for n(n-3)=65 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(n-3)=65 equation:


Simplifying
n(n + -3) = 65

Reorder the terms:
n(-3 + n) = 65
(-3 * n + n * n) = 65
(-3n + n2) = 65

Solving
-3n + n2 = 65

Solving for variable 'n'.

Reorder the terms:
-65 + -3n + n2 = 65 + -65

Combine like terms: 65 + -65 = 0
-65 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + -3n + 65 + n2 = 0 + 65

Reorder the terms:
-65 + 65 + -3n + n2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + -3n + n2 = 0 + 65
-3n + n2 = 0 + 65

Combine like terms: 0 + 65 = 65
-3n + n2 = 65

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 65 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 65 + 2.25

Combine like terms: 65 + 2.25 = 67.25
2.25 + -3n + n2 = 67.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 67.25

Calculate the square root of the right side: 8.200609733

Break this problem into two subproblems by setting 
(n + -1.5) equal to 8.200609733 and -8.200609733.

Subproblem 1

n + -1.5 = 8.200609733 Simplifying n + -1.5 = 8.200609733 Reorder the terms: -1.5 + n = 8.200609733 Solving -1.5 + n = 8.200609733 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 8.200609733 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 8.200609733 + 1.5 n = 8.200609733 + 1.5 Combine like terms: 8.200609733 + 1.5 = 9.700609733 n = 9.700609733 Simplifying n = 9.700609733

Subproblem 2

n + -1.5 = -8.200609733 Simplifying n + -1.5 = -8.200609733 Reorder the terms: -1.5 + n = -8.200609733 Solving -1.5 + n = -8.200609733 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -8.200609733 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -8.200609733 + 1.5 n = -8.200609733 + 1.5 Combine like terms: -8.200609733 + 1.5 = -6.700609733 n = -6.700609733 Simplifying n = -6.700609733

Solution

The solution to the problem is based on the solutions from the subproblems. n = {9.700609733, -6.700609733}

See similar equations:

| (x-3)(x-3)-4=18 | | 3x+90=72-9x | | -5(x+5)=65 | | 56x^2+64x+8=0 | | 5/4c=3/4 | | 2-3b-(4b-a)-5a= | | -5+4x=39 | | 16t^2+20t+6=10 | | m-2/3=1/6 | | 5w^2+10w-40=0 | | 18+x+9=18+x+9 | | 5n+12=37 | | 2y=-6x | | 190x=130x+3744 | | -3x+44=7(x+2) | | 7x+10=9x+10 | | 3(v+4)=-2v+47 | | 11r=-12r | | 7b/7=4.2 | | 7x+9y=-8 | | 4w+1=7(w+4) | | y+ax-bx=z | | 7(3s+10)=175 | | 2(2l+3)=26 | | 43x(-3x)=-240 | | 9n^2+3n-10= | | X^3-3.14X^2+3=0 | | 2-3(1-3x)=2(4x-1)+x+1 | | 11x-5y=3 | | 12x+1=45 | | n+3n-2(3n+5)=5 | | 2x-2=2(x-1)+11 |

Equations solver categories