document.write( "Question 624279: solve the following for x,
\n" ); document.write( "square root 5x-15 all under one - square root x +1 all under DISABLED_event_one= 2 \n" ); document.write( "

Algebra.Com's Answer #392667 by KMST(5328) $\"\"$ $\"About$

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$\"sqrt%285x-15%29-sqrt%28x%2B1%29=2\"$ , adding $\"sqrt%28x%2B1%29\"$ to both sides, turns into
\n" ); document.write( " $\"sqrt%285x-15%29=sqrt%28x%2B1%29%2B2\"$
\n" ); document.write( "Squaring both sides, we get $\"5x-15=x%2B1%2B4%2Asqrt%28x%2B1%29%2B4\"$
\n" ); document.write( "Adding $\"-x-5\"$ to both sides we get
\n" ); document.write( " $\"4x-20=4%2Asqrt%28x%2B1%29\"$
\n" ); document.write( "Dividing both sides by 4 we get
\n" ); document.write( " $\"x-5=sqrt%28x%2B1%29\"$
\n" ); document.write( "Suqaring both sides again, we get
\n" ); document.write( " $\"x%5E2-10x%2B25=x%2B1\"$
\n" ); document.write( "Adding $\"-x-1\"$ to both sides, we get
\n" ); document.write( " $\"x%5E2-11x%2B24=0\"$
\n" ); document.write( "Factoring, we get
\n" ); document.write( " $\"%28x-3%29%28x-8%29=0\"$
\n" ); document.write( "The solutions to $\"x%5E2-11x%2B24=0\"$ are $\"x=3\"$ and $\"x=8\"$ .
\n" ); document.write( "Those could be solutions of the original equation, or could be extraneous solutions, introduced by all that squaring of both sides.
\n" ); document.write( "We must test them in the original equation.
\n" ); document.write( " $\"x=3\"$ gives $\"sqrt%285x-15%29=0\"$ while $\"sqrt%28x%2B1%29=sqrt%284%29=2\"$ ,
\n" ); document.write( "so $\"sqrt%285x-15%29-sqrt%28x%2B1%29=-2\"$
\n" ); document.write( "showing that $\"x=3\"$ is not a solution of the original equation.
\n" ); document.write( " $\"x=8\"$ gives $\"sqrt%285x-15%29=sqrt%2840-15%29=sqrt%2825%29=5\"$ while $\"sqrt%28x%2B1%29=sqrt%289%29=3\"$ ,
\n" ); document.write( "so $\"sqrt%285x-15%29-sqrt%28x%2B1%29=5-3=2\"$
\n" ); document.write( "showing that $\"highlight%28x=8%29\"$ is the solution. \n" ); document.write( "

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