document.write( "Question 435606: I need your help with this question. A farmer has 2420 feet of fence to enclose a rectangular area that borders a river. No fence is needed along the river. Find the possibe dimensions to enclose $\"+435600+feet%5E2+\"$ . I have two equations which are x+x+y=2420 and xy=435600 and I can't figure out where to go from there. \n" ); document.write( "

Algebra.Com's Answer #301464 by edjones(8007) $\"\"$ $\"About$

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2x+y=2420
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\n" ); document.write( "y=435600/x
\n" ); document.write( "2x+(435600/x)=2420
\n" ); document.write( "2x^2+435600=2420x
\n" ); document.write( "2x^2-2420x+435600=0
\n" ); document.write( "x^2-1210x+217800=0
\n" ); document.write( "x=990, y=220 or vice versa (see below)
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B-1210x%2B217800+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-1210%29%5E2-4%2A1%2A217800=592900\"$ .
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\n" ); document.write( " Discriminant d=592900 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--1210%2B-sqrt%28+592900+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-1210%29%2Bsqrt%28+592900+%29%29%2F2%5C1+=+990\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-1210%29-sqrt%28+592900+%29%29%2F2%5C1+=+220\"$
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\n" ); document.write( " Quadratic expression $\"1x%5E2%2B-1210x%2B217800\"$ can be factored:
\n" ); document.write( " $\"1x%5E2%2B-1210x%2B217800+=+1%28x-990%29%2A%28x-220%29\"$
\n" ); document.write( " Again, the answer is: 990, 220.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1210%2Ax%2B217800+%29\"$

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