Question

How do you solve `n(n - 2) = 24`?

Answer 1

See below

Explanation:

You can afford this calculation by several ways. The simpliest is to factorize 24 in all possible ways by two factors 24=6x4 or 4x6

If it is in the first way then n=6 and then (n-2)=4

If it is in the second way n=4 and then n-2=6

The same with negative numbers because 24=(-6)(-4)=(-4)(-6)

Other way to resolve is operate in left member and you will have `n^2-2n=24` or what it's the same `n^2-2n-24=0` and you have an second degreee equation that can be resolved by the quadratic formula

`n=(2+-sqrt(4+96))/2=(2+-10)/2` with two solutions

`n=(2+10)/2=6` and
`n=(2-10)/2=-4`

Hope this help

Answer 2

`n=-4" or "n=6`

Explanation:

`"distribute and arrange in "color(blue)"standard form"`

`•color(white)(x)ax^2+bx+c=0;a!=0`

`rArrn^2-2n-24=0larrcolor(blue)"in standard form"`

`"the factors of - 24 which sum to - 2 are - 6 and + 4"`

`rArr(n-6)(n+4)=0`

`"equate each factor to zero and solve for n"`

`n-6=0rArrn=6`

`n+4=0rArrn=-4`