Question 245881
Let x = a number
Let x+2 = its consecutive odd number
.
Since the product of two consecutive odd numbers is 63, the equation becomes:
{{{x(x+2)=63}}}
.
Let's work out the algebra.
{{{x^2+2x=63}}}
{{{x^2+2x-63=0}}}
Factor:
{{{(x-7)(x+9)=0}}}
.
In order to make our above equation true, the solution set is x = {7,-9}.  
Let's check which one works for our problem:
.
{{{x(x+2)=63}}}
{{{7(7+2)=63}}}
{{{7*9=63}}}
{{{63=63}}}  <--- 7 works!
So, x=7 and x+2=9.
.
{{{x(x+2)=63}}}
{{{-9(-9+2)=63}}}
{{{-9(-7)=63}}}
{{{63=63}}}  <--- -9 also works!
So, x=-9 and x+2=-7.
.
Both solution sets fit our criteria.  
Both are odd numbers and both are odd consecutives which product is 63.