document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=509175>Question 509175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 26.Solve.<BR>\n" );
document.write( "15t^2 + 7t = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve:#14<BR>\n" );
document.write( "Rowing. Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still water.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "My math friends please help me with these I am on a deadline, thank you.I really am desperate here. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341312 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=341312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 26.Solve.<BR>\n" );
document.write( "15t^2 + 7t = 2<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "15t^2 + 7t - 2 = 0<BR>\n" );
document.write( "(3t + 2)*(5t - 1) = 0<BR>\n" );
document.write( "t = -2/3, 1/5<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Solve:#14<BR>\n" );
document.write( "Rowing. Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still water.<BR>\n" );
document.write( "10/(b-5) + 10/(b+5) = 3<BR>\n" );
document.write( "10(b+5) + 10(b-5) = 3*(b-5)*(b+5) = 3b^2 - 75<BR>\n" );
document.write( "20b = 3b^2 - 75<BR>\n" );
document.write( "3b^2 - 20b - 75 = 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=3x%5E2%2B-20x%2B-75+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-20x%2B-75+=+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=%28-20%29%5E2-4%2A3%2A-75=1300 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-20%29%5E2-4%2A3%2A-75=1300\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1300 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--20%2B-sqrt%28+1300+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--20%2B-sqrt%28+1300+%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-%28-20%29%2Bsqrt%28+1300+%29%29%2F2%5C3+=+9.34258545910665 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+1300+%29%29%2F2%5C3+=+9.34258545910665\"   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-%28-20%29-sqrt%28+1300+%29%29%2F2%5C3+=+-2.67591879243998 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-20%29-sqrt%28+1300+%29%29%2F2%5C3+=+-2.67591879243998\"   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=3x%5E2%2B-20x%2B-75 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-20x%2B-75\"   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=3x%5E2%2B-20x%2B-75+=+%28x-9.34258545910665%29%2A%28x--2.67591879243998%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-20x%2B-75+=+%28x-9.34258545910665%29%2A%28x--2.67591879243998%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9.34258545910665, -2.67591879243998.\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+3%2Ax%5E2%2B-20%2Ax%2B-75+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-20%2Ax%2B-75+%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( "speed =~ 9.34 km/hr </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );