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

1 Answer

Mar 3, 2016

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 $-19$ .

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