document.write( "Question 874864: Sqrt(5x+1)-sqrt(x)=5 \n" ); document.write( "
Algebra.Com's Answer #527806 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"sqrt%285x%2B1%29-sqrt%28x%29=5\"\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%285x%2B1%29=5%2Bsqrt%28x%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28sqrt%285x%2B1%29%29%5E2=%285%2Bsqrt%28x%29%29%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"5x%2B1=%285%2Bsqrt%28x%29%29%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"5x%2B1=25%2B10%2Asqrt%28x%29%2Bx\"\r
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\n" ); document.write( "\n" ); document.write( "\"5x%2B1-25-x=10%2Asqrt%28x%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"4x-24=10%2Asqrt%28x%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%284x-24%29%5E2=%2810%2Asqrt%28x%29%29%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"%284x-24%29%5E2=100x\"\r
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\n" ); document.write( "\n" ); document.write( "\"16x%5E2-192x%2B576=100x\"\r
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\n" ); document.write( "\n" ); document.write( "\"16x%5E2-192x%2B576-100x=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"16x%5E2-292x%2B576=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"4%284x-9%29%28x-16%29=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"4x-9=0\" or \"x-16=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"x=9%2F4\" or \"x=16\"\r
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\n" ); document.write( "\n" ); document.write( "The *possible* solutions are \"x=9%2F4\" or \"x=16\"\r
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\n" ); document.write( "\n" ); document.write( "However, you'll find that plugging \"x=9%2F4\" back into \"sqrt%285x%2B1%29-sqrt%28x%29=5\" results in a false equation (I'll let you do that part).\r
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\n" ); document.write( "\n" ); document.write( "Plugging \"x=16\" into \"sqrt%285x%2B1%29-sqrt%28x%29=5\" results in a true equation (I'll let you do that part as well).\r
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\n" ); document.write( "\n" ); document.write( "So that means \"x=16\" is the only solution.
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