document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=582171>Question 582171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what speed will the car need to travel to use 200 horsepower to overcome the wind drag?<BR>\n" );
document.write( "I tried this several ways and still came up with 199.32 miles per hour which my teacher says is wrong.<BR>\n" );
document.write( "Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371967 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what speed will the car need to travel to use 200 horsepower to overcome the wind drag?<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "H=0.005s^2 + 0.007s - 0.031<BR>\n" );
document.write( "0.005s^2 + 0.007s - 0.031 = 200<BR>\n" );
document.write( "5s^2 + 7s - 31 = 200000<BR>\n" );
document.write( "5s^2 + 7s - 200031 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B7x%2B-200031+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B7x%2B-200031+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%287%29%5E2-4%2A5%2A-200031=4000669 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%287%29%5E2-4%2A5%2A-200031=4000669\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4000669 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-7%2B-sqrt%28+4000669+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-7%2B-sqrt%28+4000669+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%287%29%2Bsqrt%28+4000669+%29%29%2F2%5C5+=+199.316724300744 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%287%29%2Bsqrt%28+4000669+%29%29%2F2%5C5+=+199.316724300744\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%287%29-sqrt%28+4000669+%29%29%2F2%5C5+=+-200.716724300744 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%287%29-sqrt%28+4000669+%29%29%2F2%5C5+=+-200.716724300744\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B7x%2B-200031 ALIGN=MIDDLE  ALT=\"5x%5E2%2B7x%2B-200031\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B7x%2B-200031+=+%28x-199.316724300744%29%2A%28x--200.716724300744%29 ALIGN=MIDDLE  ALT=\"5x%5E2%2B7x%2B-200031+=+%28x-199.316724300744%29%2A%28x--200.716724300744%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 199.316724300744, -200.716724300744.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B7%2Ax%2B-200031+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B7%2Ax%2B-200031+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "====================<BR>\n" );
document.write( "Ignore the negative solution.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "I get the same answer.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );