document.write( "Question 245881: The product of 2 consecutive odd numbers is 63. What is the larger number? \n" ); document.write( "

Algebra.Com's Answer #179538 by College Student(505) $\"\"$ $\"About$

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Let x = a number
\n" ); document.write( "Let x+2 = its consecutive odd number
\n" ); document.write( ".
\n" ); document.write( "Since the product of two consecutive odd numbers is 63, the equation becomes:
\n" ); document.write( " $\"x%28x%2B2%29=63\"$
\n" ); document.write( ".
\n" ); document.write( "Let's work out the algebra.
\n" ); document.write( " $\"x%5E2%2B2x=63\"$
\n" ); document.write( " $\"x%5E2%2B2x-63=0\"$
\n" ); document.write( "Factor:
\n" ); document.write( " $\"%28x-7%29%28x%2B9%29=0\"$
\n" ); document.write( ".
\n" ); document.write( "In order to make our above equation true, the solution set is x = {7,-9}.
\n" ); document.write( "Let's check which one works for our problem:
\n" ); document.write( ".
\n" ); document.write( " $\"x%28x%2B2%29=63\"$
\n" ); document.write( " $\"7%287%2B2%29=63\"$
\n" ); document.write( " $\"7%2A9=63\"$
\n" ); document.write( " $\"63=63\"$ <--- 7 works!
\n" ); document.write( "So, x=7 and x+2=9.
\n" ); document.write( ".
\n" ); document.write( " $\"x%28x%2B2%29=63\"$
\n" ); document.write( " $\"-9%28-9%2B2%29=63\"$
\n" ); document.write( " $\"-9%28-7%29=63\"$
\n" ); document.write( " $\"63=63\"$ <--- -9 also works!
\n" ); document.write( "So, x=-9 and x+2=-7.
\n" ); document.write( ".
\n" ); document.write( "Both solution sets fit our criteria.
\n" ); document.write( "Both are odd numbers and both are odd consecutives which product is 63. \n" ); document.write( "

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