document.write( "Question 449726: square root of (2x+3) = x
\n" ); document.write( "I got x = -1, 3 but my answer sheet says only x = 3 WHY? \n" ); document.write( "

Algebra.Com's Answer #309350 by Leaf W.(135) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%282x+%2B+3%29+=+x\"$
\n" ); document.write( "You found the solutions correctly, but you must check your answers in all square-root equations like this.
\n" ); document.write( "-1 is not an answer because:
\n" ); document.write( " $\"sqrt%282%28-1%29+%2B+3%29+=+-1\"$
\n" ); document.write( " $\"sqrt%28-2+%2B+3%29+=+-1\"$
\n" ); document.write( " $\"sqrt%281%29+=+-1\"$
\n" ); document.write( " $\"1+=+-1\"$ <== FALSE!
\n" ); document.write( "Sure, if you multiply -1*-1, that equals 1, so technically $\"sqrt%281%29+=+-1\"$ is correct, but in order to avoid confusion, people have decided to denote only a positive number x as $\"sqrt%28x%5E2%29\"$ ; negative x is denoted as $\"-sqrt%28x%5E2%29\"$ . For example:
\n" ); document.write( "5 is denoted as $\"sqrt%2825%29\"$
\n" ); document.write( "-5 is denoted as $\"-sqrt%2825%29\"$ , NOT $\"sqrt%2825%29\"$
\n" ); document.write( "Since $\"sqrt%282%283%29+%2B+3%29+=+3\"$
\n" ); document.write( " $\"sqrt%286+%2B+3%29+=+3\"$
\n" ); document.write( " $\"sqrt%289%29+=+3\"$
\n" ); document.write( " $\"3+=+3\"$ is correct,
\n" ); document.write( "***The only solution for x is 3.
\n" ); document.write( "I hope that makes sense! =) \n" ); document.write( "

\n" );