document.write( "Question 152194: The sum of the number and its square is twelve times the next higher number. Find the no. \n" ); document.write( "

Algebra.Com's Answer #111867 by orca(409) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the number be n, then the next higher number is n + 1
\n" ); document.write( "The sum of the number and its square can be written as n + n^2.
\n" ); document.write( "Twelve times the next higher number can be expressed as 12(n + 1).
\n" ); document.write( "As the sum of the number and its square is twelve times the next higher number, we have:
\n" ); document.write( "n + n^2 = 12(n + 1)
\n" ); document.write( "Solving the quadratic equation for x, we have
\n" ); document.write( "n + n^2 = 12n + 12
\n" ); document.write( "n^2 - 11n - 12 = 0
\n" ); document.write( "(n - 12)(n + 1) = 0
\n" ); document.write( "So n = 12 or n = -1
\n" ); document.write( "Therefore the number is 12 or -1.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );