document.write( "Question 1036328: Solve:
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\n" ); document.write( "\n" ); document.write( "some rationalisation, surds? Not sure how to do this. Any help appreciated.
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Algebra.Com's Answer #650998 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"3-5x+=+sqrt%285%29\"\r\n" );
document.write( "Square both sides\r\n" );
document.write( "\"%283-5x%29%5E2+=+%28sqrt%285%29%29%5E2\"\r\n" );
document.write( "Simplify\r\n" );
document.write( "\"%283-5x%29%283-5x%29+=+5\"\r\n" );
document.write( "\"9-15x-15x%2B25x%5E2=5\"\r\n" );
document.write( "\"9-30x%2B25x%5E2=5\"\r\n" );
document.write( "Subtract 5 from both sides to get 0 on the right\r\n" );
document.write( "\"4-30x%2B25x%5E2=0\"\r\n" );
document.write( "Rearrange terms in descending order:\r\n" );
document.write( "\"25x%5E2-30x%2B4=0\"\r\n" );
document.write( "Use the quadratic formula:\r\n" );
document.write( " \"x+=+%28-b+%2B-+sqrt%28b%5E2-4ac+%29%29%2F%282a%29+\"\r\n" );
document.write( " \"x+=+%28-%28-30%29+%2B-+sqrt%28%28-30%29%5E2-4%2825%29%284%29+%29%29%2F%282%2825%29%29+\"\r\n" );
document.write( " \"x+=+%2830+%2B-+sqrt%28900-400+%29%29%2F50+\"\r\n" );
document.write( " \"x+=+%2830+%2B-+sqrt%28500%29%29%2F50+\"\r\n" );
document.write( " \"x+=+%2830+%2B-+sqrt%28100%2A5%29%29%2F50+\"\r\n" );
document.write( " \"x+=+%2830+%2B-+10sqrt%285%29%29%2F50+\"\r\n" );
document.write( "Factor out 10 in the numerator:\r\n" );
document.write( " \"x+=+%2810%283+%2B-+sqrt%285%29%29%29%2F50+\"\r\n" );
document.write( "Divide top and bottom by 10\r\n" );
document.write( " \"x+=+%283+%2B-+sqrt%285%29%29%2F5+\"\r\n" );
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document.write( "Using the +:\r\n" );
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document.write( " \"x+=+%283+%2B+sqrt%285%29%29%2F5+\"\r\n" );
document.write( " \"x+=+%283+%2B+2.236%29%2F5+\"\r\n" );
document.write( " \"x+=+%285.236%29%2F5+\"\r\n" );
document.write( " \"x+=+1.0472+\"\r\n" );
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document.write( "Checking in the original equation:\r\n" );
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document.write( "\"3-5x+=+sqrt%285%29\"\r\n" );
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document.write( "\"3-5%281.0472%29+=+2.236\"\r\n" );
document.write( "\"3-5.236+=+2.236\"\r\n" );
document.write( "\"-2.236+=+2.236\"\r\n" );
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document.write( "That doesn't check so we must discard  \"cross%28x+=+%283+%2B+sqrt%285%29%29%2F5%29+\"\r\n" );
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document.write( "Using the -:\r\n" );
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document.write( " \"x+=+%283+-+sqrt%285%29%29%2F5+\"\r\n" );
document.write( " \"x+=+%283+-+2.236%29%2F5+\"\r\n" );
document.write( " \"x+=+%28.764%29%2F5+\"\r\n" );
document.write( " \"x+=+0.1528+\"\r\n" );
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document.write( "Checking in the original equation:\r\n" );
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document.write( "\"3-5x+=+sqrt%285%29\"\r\n" );
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document.write( "\"3-5%280.1528%29+=+2.236\"\r\n" );
document.write( "\"3-0.764+=+2.236\"\r\n" );
document.write( "\"2.236+=+2.236\"\r\n" );
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document.write( "That checks, so the only solution is  \"x+=+%283+-+sqrt%285%29%29%2F5+\"\r\n" );
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document.write( "Note, you must always check equations with square roots\r\n" );
document.write( "because oftentimes there are extraneous \"answers\".\r\n" );
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document.write( "Edwin

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