document.write( "Question 155290: Solve the equation. Check for extraneous solutions.\r
\n" ); document.write( "\n" ); document.write( "square root of 5x+1 = x-4 \n" ); document.write( "

Algebra.Com's Answer #114376 by oscargut(2103) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%285x%2B1%29=x-4\"$
\n" ); document.write( "then
\n" ); document.write( " $\"5x%2B1=%28x-4%29%5E2\"$
\n" ); document.write( "then
\n" ); document.write( " $\"5x%2B1=x%5E2-8x%2B16\"$
\n" ); document.write( "then
\n" ); document.write( " $\"-x%5E2%2B13x-15=0\"$
\n" ); document.write( "then
\n" ); document.write( " $\"x+=+%28-13+%2B-+sqrt%28+13%5E2-4%2A%28-1%29%2A%28-15%29+%29%29%2F%282%2A%28-1%29%29+\"$
\n" ); document.write( "then
\n" ); document.write( " $\"x+=+%28-13+%2B-+sqrt%28+13%5E2-4%2A%28-1%29%2A%28-15%29+%29%29%2F%282%2A%28-1%29%29+\"$
\n" ); document.write( "then
\n" ); document.write( " $\"x+=+%28-13+%2B-+sqrt%28109%29%29%2F%28-2%29+\"$
\n" ); document.write( "x=11.72 (aprox) or x=1.28 (aprox)\r
\n" ); document.write( "\n" ); document.write( "Checking:
\n" ); document.write( "x-4 is positive if x=11.72 but is negative if x=1.28
\n" ); document.write( " $\"sqrt%285x%2B1%29\"$ is always positive so x=1.28 is a extraneous solution
\n" ); document.write( "and the only solution for the first equation is the first\r
\n" ); document.write( "\n" ); document.write( "Answer: $\"x+=+%28-13+-+sqrt%28109%29%29%2F%28-2%29+\"$ \r
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