document.write( "Question 202155: When the sum of a number plus 3 is squared, it is 13 more than the sum of the number plus 2 when squared. \n" ); document.write( "

Algebra.Com's Answer #152406 by Earlsdon(6294) $\"\"$ $\"About$

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Let n = the required number, so...
\n" ); document.write( " $\"%28n%2B3%29%5E2+=+%28n%2B2%29%5E2%2B13\"$ Expand.
\n" ); document.write( " $\"n%5E2%2B6n%2B9+=+n%5E2%2B4n%2B4%2B13\"$ Subtract $\"n%5E2\"$ from both sides.
\n" ); document.write( " $\"6n%2B9+=+4n%2B17\"$ Subtract 4n from both sides.
\n" ); document.write( " $\"2n%2B9+=+17\"$ Subtract 9 from both sides.
\n" ); document.write( " $\"2n+=+8\"$ Finally, divide both sides by 2.
\n" ); document.write( " $\"highlight%28n+=+4%29\"$
\n" ); document.write( "Check:
\n" ); document.write( " $\"%28n%2B3%29%5E2+=+%28n%2B2%29%5E2%2B13\"$ Substitute n = 4.
\n" ); document.write( " $\"%284%2B3%29%5E2+=+%284%2B2%29%5E2%2B13\"$ Evaluate.
\n" ); document.write( " $\"49+=+36%2B13\"$
\n" ); document.write( " $\"49+=+49\"$ OK! \n" ); document.write( "

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