The product of two consecutive odd integers is 63 find all such pairs of integers

X= first consecutive odd integer
x+2= second consecutive odd integer
product= multiply

x(x + 2)= 63
multiply x by all terms in parentheses

(x*x) + (x*2)= 63
multiply in parentheses

x^2 + 2x= 63
subtract 63 from both sides

x^2 + 2x - 63= 0
factor

(x + 9)(x - 7)= 0
set each parentheses equal to 0

x + 9= 0
x= -9

x - 7= 0
x= 7

-9 and 7 could each be the first consecutive odd integer. Add 2 to each to find the second consecutive odd integer.

ANSWER: since the question did not say if the integers were positive or negative, the possible pairs of consecutive odd integers are:

x= -9; x + 2= -7

x= 7; x + 2= 9

Hope this helps! :)

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