Solve equation (2x+1)A2=110

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use factorial formula of arrangements of `n`  elements taken `k`  at a time such that:

`A_n^k = (n!)/((n-k)!)`

Substituting `2x + 1`  for `n`  and `2`  for `k`  yields:

`A_(2x+1)^2= ((2x+1)!)/((2x+1-2)!)`

`A_(2x+1)^2 = ((2x+1)!)/((2x-1)!)`

You may write `(2x+1)!`  as `(2x-1)!(2x)(2x+1)`  such that:

`A_(2x+1)^2 = ((2x-1)!(2x)(2x+1))/((2x-1)!)`

Reducing like terms yields:

`A_(2x+1)^2 = 2x(2x+1)`

Substituting `2x(2x+1)`  for  `A_(2x+1)^2`  in equation yields:

`2x(2x+1) = 110`

Reducing by 2 both sides yields:

`x(2x+1) = 55`

You need to open brackets such that:

`2x^2 + x = 55 =gt 2x^2 + x- 55 = 0`

You need to use quadratic formula such that:

`x_(1,2) = (-1+-sqrt(1+440))/4 =gt x_(1,2) = (-1+-21)/4`

`x_1 = 5 ; x_2 = -22/4 =gt x_2 = -11/2`

You need to keep only the natural number `5` , hence the solution to the equation is `x=5` .

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