document.write( "Question 301003: Quadratic application
\n" ); document.write( "If the cost ,C(x) for manufactoring x units of a certain product is given by \r
\n" ); document.write( "\n" ); document.write( "C(x)=x^2-125x+50, find thye units manufactored at a cost of $9500 \n" ); document.write( "
Algebra.Com's Answer #215865 by nerdybill(7384)\"\" \"About 
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If the cost ,C(x) for manufactoring x units of a certain product is given by
\n" ); document.write( "C(x)=x^2-125x+50, find thye units manufactored at a cost of $9500
\n" ); document.write( ".
\n" ); document.write( "The given quadratic:
\n" ); document.write( "C(x)=x^2-125x+50
\n" ); document.write( "where
\n" ); document.write( "C(x) is the cost
\n" ); document.write( "x is the number of units
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\n" ); document.write( "Simply plug in the given cost and solve for x:
\n" ); document.write( "C(x)=x^2-125x+50
\n" ); document.write( "9500 = x^2-125x+50
\n" ); document.write( "0 = x^2-125x-9450
\n" ); document.write( "Apply the quadratic formula when then yields:
\n" ); document.write( "x = {178.07, -53.07}
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\n" ); document.write( "Throw out the negative solution leaving:
\n" ); document.write( "x = 178 units
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\n" ); document.write( "Details of quadratic formula follows:
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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-125x%2B-9450+=+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=%28-125%29%5E2-4%2A1%2A-9450=53425\".
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\n" ); document.write( " Discriminant d=53425 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--125%2B-sqrt%28+53425+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-125%29%2Bsqrt%28+53425+%29%29%2F2%5C1+=+178.069243313262\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-125%29-sqrt%28+53425+%29%29%2F2%5C1+=+-53.0692433132622\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-125x%2B-9450\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-125x%2B-9450+=+1%28x-178.069243313262%29%2A%28x--53.0692433132622%29\"
\n" ); document.write( " Again, the answer is: 178.069243313262, -53.0692433132622.\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-125%2Ax%2B-9450+%29\"
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