document.write( "Question 62139: sqrt(2x+3) - sqrt(x+1) = 1, solve for x ( could be 2 solutions) \n" ); document.write( "

Algebra.Com's Answer #42909 by joyofmath(189) $\"\"$ $\"About$

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sqrt(2x+3) - sqrt(x+1) = 1, solve for x ( could be 2 solutions)\r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%282x%2B3%29+-+sqrt%28x%2B1%29+=+1\"$ .
\n" ); document.write( " $\"sqrt%282x%2B3%29+=+1%2Bsqrt%28x%2B1%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "Square both sides:\r
\n" ); document.write( "\n" ); document.write( " $\"2x%2B3+=+1+%2B+2sqrt%28x%2B1%29+%2B+x%2B1\"$ .\r
\n" ); document.write( "\n" ); document.write( "Combine like terms:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2B1+=+2sqrt%28x%2B1%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "Square both sides again:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2x%2B1+=+4%28x%2B1%29+=+4x%2B4\"$ .\r
\n" ); document.write( "\n" ); document.write( "Turn this into the form of a quadratic equation:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2+-+2x+-+3+=+0+\"$ .\r
\n" ); document.write( "\n" ); document.write( "This equation factors: $\"%28x%2B1%29%28x-3%29\"$ .
\n" ); document.write( "So, $\"x+=+-1\"$ or $\"x+=+3\"$ .\r
\n" ); document.write( "\n" ); document.write( "Let's verify these answers:\r
\n" ); document.write( "\n" ); document.write( "When x = -1 then $\"sqrt%282x%2B3%29+-+sqrt%28x%2B1%29+=+sqrt%281%29+-+sqrt%280%29+=+1\"$ .
\n" ); document.write( "When x = 3 then $\"sqrt%282x%2B3%29+-+sqrt%28x%2B1%29+=+sqrt%289%29+-+sqrt%284%29+=+3+-+2+=+1\"$ . \n" ); document.write( "

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