document.write( "Question 163715: I am looking for the width of a golden rectangle where the length is given as
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\n" ); document.write( "The formula I have been given is \"L%2FW+=+W%2F%28L-W%29\" where length divided by
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Algebra.Com's Answer #120606 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Plug in 36 for the length L into\r\n" );
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document.write( "\"L%2FW+=+W%2F%28L-W%29\"\r\n" );
document.write( "\"36%2FW+=+W%2F%2836-W%29\"\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "\"36%2836-W%29=W%5E2\"\r\n" );
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document.write( "\"1296-36W=W%5E2\"\r\n" );
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document.write( "Get 0 on the left, by adding -1296\r\n" );
document.write( "and +36W to both sides:\r\n" );
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document.write( "\"0=W%5E2%2B36W-1296\"\r\n" );
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document.write( "Swap sides:\r\n" );
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document.write( "\"W%5E2%2B36W-1296=0\"\r\n" );
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document.write( "That doesn't factor, so we use the\r\n" );
document.write( "quadratic formula:\r\n" );
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document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" \r\n" );
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document.write( " with\r\n" );
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document.write( "\"matrix%281%2C7%2C+x=W%2C+%22%2C%22%2C+a=1%2C%22%2C%22%2C+b=36%2C%22%2C%22%2C+c=-1296%29\"\r\n" );
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document.write( "\"W+=+%28-36+%2B-+sqrt%28+6480+%29%29%2F2+\"\r\n" );
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document.write( "\"W+=+%28-36+%2B-+sqrt%281296%2A5%29%29%2F2+\"\r\n" );
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document.write( "\"W+=+%28-36+%2B-+sqrt%281296%29sqrt%285%29%29%2F2+\"\r\n" );
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document.write( "\"W+=+%28-36+%2B-+36sqrt%285%29%29%2F2+\"\r\n" );
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document.write( "Write as the sum of two fractions:\r\n" );
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document.write( "\"W+=+-36%2F2+%2B-+36sqrt%285%29%2F2+\"\r\n" );
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document.write( "\"W+=+-18+%2B-+18sqrt%285%29+\"\r\n" );
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document.write( "Simplify the second term by dividing 18 and 2 by 2\r\n" );
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document.write( "\"W+=+-18+%2B-+18sqrt%285%29+\"\r\n" );
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document.write( "That's OK like that or you may factor out\r\n" );
document.write( "9:\r\n" );
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document.write( "\"W+=+18%28-1+%2B-+sqrt%285%29%29+\"\r\n" );
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document.write( "Using the plus:\r\n" );
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document.write( "\"W+=+18%28-1+%2B+sqrt%285%29%29+=+22.24922359\", approximately.\r\n" );
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document.write( "Using the minus:\r\n" );
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document.write( "\"W+=+9%28-1+-+sqrt%285%29%29+=+-58.24922359\", approximately.\r\n" );
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document.write( "We can discard the negative answer, since a rectangle\r\n" );
document.write( "cannot have a negative side, and the width is given by:\r\n" );
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document.write( "\"W+=+18%28-1+%2B+sqrt%285%29%29+=+22.24922359\" inches, approximately.\r\n" );
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document.write( "Edwin
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