document.write( "Question 289537: sqrt(x)+ sqrt(x-5)=sqrt(2x+7) \n" ); document.write( "

Algebra.Com's Answer #209669 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%28x%29%2B+sqrt%28x-5%29=sqrt%282x%2B7%29\"$
\n" ); document.write( "Square both sides.
\n" ); document.write( " $\"%28sqrt%28x%29%2Bsqrt%28x-5%29%29%5E2=2x%2B7\"$
\n" ); document.write( "

\n" ); document.write( " $\"x%2B2sqrt%28x%29sqrt%28x-5%29%2B%28x-5%29=2x%2B7\"$
\n" ); document.write( " $\"2x-5%2B2sqrt%28x%29sqrt%28x-5%29=2x%2B7\"$
\n" ); document.write( " $\"2sqrt%28x%29sqrt%28x-5%29=12\"$
\n" ); document.write( " $\"sqrt%28x%29sqrt%28x-5%29=6\"$
\n" ); document.write( "Square both sides.
\n" ); document.write( " $\"x%28x-5%29=36\"$
\n" ); document.write( " $\"x%5E2-5x=36\"$
\n" ); document.write( " $\"x%5E2-5x-36=0\"$
\n" ); document.write( "Factor.
\n" ); document.write( " $\"%28x-9%29%28x%2B4%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x-9=0\"$
\n" ); document.write( " $\"x=9\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"x%2B4=0\"$
\n" ); document.write( " $\"x=-4\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Go back and verify the solutions.
\n" ); document.write( " $\"+x=9\"$
\n" ); document.write( " $\"+sqrt%28x%29%2B+sqrt%28x-5%29=sqrt%282x%2B7%29\"$
\n" ); document.write( " $\"+sqrt%289%29%2B+sqrt%289-5%29=sqrt%282%289%29%2B7%29\"$
\n" ); document.write( " $\"+3%2Bsqrt%284%29=sqrt%2825%29\"$
\n" ); document.write( " $\"+3%2B2=5\"$
\n" ); document.write( " $\"+5=5\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"+x=-4\"$
\n" ); document.write( "Not a solution since the square root of a negative number in undefined.
\n" ); document.write( " \n" ); document.write( "

\n" );