document.write( "Question 50015: twice a number is 8 less than its square. what is the number? \n" ); document.write( "

Algebra.Com's Answer #33249 by Earlsdon(6294) $\"\"$ $\"About$

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Let the required number(s) be n.\r
\n" ); document.write( "\n" ); document.write( "From the problem description, you can write:
\n" ); document.write( " $\"2n+=+n%5E2-8\"$ Subtract 2n from both sides.
\n" ); document.write( " $\"n%5E2-2n-8+=+0\"$ Solve by factoring.
\n" ); document.write( " $\"%28n%2B2%29%28n-4%29+=+0\"$ Apply the zero product principle.
\n" ); document.write( " $\"n%2B2+=+0\"$ and/or $\"n-4+=+0\"$
\n" ); document.write( "If $\"n%2B2+=+0\"$ then $\"n+=+-2\"$
\n" ); document.write( "If $\"n-4+=+0\"$ then $\"n+=+4\"$ \r
\n" ); document.write( "\n" ); document.write( "There are two solutions to this problem:\r
\n" ); document.write( "\n" ); document.write( "n = -2 and
\n" ); document.write( "n = 4\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "n = -2
\n" ); document.write( " $\"2%28-2%29+=+%28-2%29%5E2-8\"$
\n" ); document.write( " $\"-4+=+4-8\"$
\n" ); document.write( " $\"-4+=+-4\"$ \r
\n" ); document.write( "\n" ); document.write( "n = 4\r
\n" ); document.write( "\n" ); document.write( " $\"2%284%29+=+%284%29%5E2-8\"$
\n" ); document.write( " $\"8+=+16-8\"$
\n" ); document.write( " $\"8+=+8\"$ \r
\n" ); document.write( "\n" ); document.write( "Both solutions work. \n" ); document.write( "

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