document.write( "Question 49955: $\"+sqrt%28+x%2B1+%29+\"$ = $\"+sqrt%28+x%2B6+%29+\"$ -1 \n" ); document.write( "

Algebra.Com's Answer #33197 by Earlsdon(6294) $\"\"$ $\"About$

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Solve:
\n" ); document.write( " $\"sqrt%28x%2B1%29+=+sqrt%28x%2B6%29-1\"$ First, square both sides.
\n" ); document.write( " $\"x%2B1+=+%28x%2B6%29-2sqrt%28x%2B6%29%2B1\"$ Simplify.
\n" ); document.write( " $\"x%2B1+=+%28x%2B1%29%2B6-2sqrt%28x%2B6%29\"$ Subtract (x+1) from both sides.
\n" ); document.write( " $\"0+=+6-2sqrt%28x%2B6%29\"$ Add $\"2sqrt%28x%2B6%29\"$ to both sides.
\n" ); document.write( " $\"2sqrt%28x%2B6%29+=+6\"$ Divide both sides by 2.
\n" ); document.write( " $\"sqrt%28x%2B6%29+=+3\"$ Now square both sides.
\n" ); document.write( " $\"x%2B6+=+9\"$ Finally, subtract 6 from both sides.
\n" ); document.write( " $\"x+=+3\"$ \r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( " $\"sqrt%283%2B1%29+=+sqrt%283%2B6%29-1\"$
\n" ); document.write( " $\"sqrt%284%29+=+sqrt%289%29-1\"$
\n" ); document.write( " $\"2+=+3-1\"$
\n" ); document.write( " $\"2+=+2\"$ \n" ); document.write( "

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