document.write( "Question 238098: The length of Jim's leader is always 2 feet shorter than the length of his fishing rod. If the product of the length of the leader and the length of the rod equals the strength of his line in pounds and he uses a 16-lb line, what is the length of his leader?
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Algebra.Com's Answer #174973 by Stitch(470)\"\" \"About 
You can put this solution on YOUR website!
Let X = the length of the rod
\n" ); document.write( "Let Y = the length of the leader
\n" ); document.write( "Equation 1: \"Y+=+X+-+2\"
\n" ); document.write( "Equation 2: \"X+%2A+Y+=+16\"\r
\n" ); document.write( "\n" ); document.write( "Using equation 1, plug (X - 2) into equation 2 for Y
\n" ); document.write( "\"X+%2A+Y+=+16\"
\n" ); document.write( "\"X+%2A+%28X+-+2%29+=+16\" Rewrite the equation
\n" ); document.write( "\"X%5E2+-+2X+=+16\" Subtract 16 form both sides
\n" ); document.write( "\"X%5E2+-+2X+-+16+=+0\" Then you need to use the quadratic equation
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"aX%5E2%2BbX%2Bc=0\" (in our case \"1X%5E2%2B-2X%2B-16+=+0\") has the following solutons:
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\n" ); document.write( " \"X%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-16=68\".
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\n" ); document.write( " Discriminant d=68 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--2%2B-sqrt%28+68+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"X%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+5.12310562561766\"
\n" ); document.write( " \"X%5B2%5D+=+%28-%28-2%29-sqrt%28+68+%29%29%2F2%5C1+=+-3.12310562561766\"
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\n" ); document.write( " Quadratic expression \"1X%5E2%2B-2X%2B-16\" can be factored:
\n" ); document.write( " \"1X%5E2%2B-2X%2B-16+=+1%28X-5.12310562561766%29%2A%28X--3.12310562561766%29\"
\n" ); document.write( " Again, the answer is: 5.12310562561766, -3.12310562561766.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-16+%29\"

\n" ); document.write( "\n" ); document.write( "Since you can not have a negative length, the 5.123 is the only rational answer.
\n" ); document.write( "But remember that 5.123 is the length of the rod.
\n" ); document.write( "To find the length of the leader, plug 5.123 into equation 1 for X
\n" ); document.write( "Equation 1: \"Y+=+X+-+2\"
\n" ); document.write( "\"Y+=+5.123+-+2\"
\n" ); document.write( "\"highlight+%28Y+=+3.123%29\"
\n" ); document.write( "The leader = 3.123ft
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