Question

The product of two consecutive odd numbers is 399, what are the numbers?

Answer 1

solution set `1`: `19` and `21`
solution set `2`: `-21` and `-19`

Explanation:

`1`. Make `2` let statements to represent the variables to be used in the algebraic equation.

Let `color(red)x` represent the first number.
Let `color(blue)(x+2)` represent the second number.

`2`. Form an equation.

`color(red)x(color(blue)(x+2))=399`

`3`. Isolate for `x`.

`x^2+2x=399`

`x^2+2x-399=0`

`4`. Factor the quadratic trinomial.

`(x-19)(x+21)=0`

`5`. Set each factor to `0` to determine the possible values for `x`.

`x-19=0color(white)(XXXXXXXX)x+21=0`

`x=19color(white)(XXXXXXXXXX)x=-21`

`6`. Substitute `x=19,-21` into `color(blue)(x+2)` to determine the second numbers.

`color(blue)(x+2)color(white)(XXXXXXXXXXx)color(blue)(x+2)`

`=19+2color(white)(XXXXXXXX)=-21+2`

`=21color(white)(XXXXXXXXXX)=-19`

`:.`, the numbers are `19` and `21` or `-21` and `-19`.