document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515573>Question 515573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble trying to solve this problem.  Would someobdy be able to assist me?\r<BR>\n" );
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document.write( "Solve - 3x^2 - 7x - 5 = 0<BR>\n" );
document.write( "a.  The solutions(s) is/are x=?<BR>\n" );
document.write( "b.  Find the x-intercepts of f(x) = 3x^2 -7x - 5.\r<BR>\n" );
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document.write( "1/3 x 3x^2 - 7/3x - 5/3 = 0<BR>\n" );
document.write( "x^2 - 7/3x - 5/3 = 0<BR>\n" );
document.write( "x^2 - 7/3x - 5/3  this is where I get lost.\r<BR>\n" );
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document.write( "Thank you.\r<BR>\n" );
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document.write( "Sincerely,\r<BR>\n" );
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document.write( "Christine Fitzgerald </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344074 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=344074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the x-intercepts of f(x) = 3x^2 -7x - 5. <BR>\n" );
document.write( "1/3 x 3x^2 - 7/3x - 5/3 = 0<BR>\n" );
document.write( "x^2 - 7/3x - 5/3 = 0<BR>\n" );
document.write( "x^2 - 7/3x - 5/3 this is where I get lost. <BR>\n" );
document.write( "Add 5/3 to both sides<BR>\n" );
document.write( "x^2 - 7/3x = 5/3<BR>\n" );
document.write( "To complete the square, you have to add c, which is (b/2a)^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+%28%28-7%2F3%29%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"c+=+%28%28-7%2F3%29%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c = 49/36<BR>\n" );
document.write( "Add that to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+7%2F3x+%2B+49%2F36+=+5%2F3+%2B+49%2F36+=+109%2F36 ALIGN=MIDDLE  ALT=\"x%5E2+-+7%2F3x+%2B+49%2F36+=+5%2F3+%2B+49%2F36+=+109%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+7%2F6%29%5E2+=+109%2F36 ALIGN=MIDDLE  ALT=\"%28x+-+7%2F6%29%5E2+=+109%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+7%2F6+=+sqrt%28109%29%2F6 ALIGN=MIDDLE  ALT=\"x+-+7%2F6+=+sqrt%28109%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F6+%2B+sqrt%28109%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+7%2F6+%2B+sqrt%28109%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F6+-+sqrt%28109%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+7%2F6+-+sqrt%28109%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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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-7x%2B-5+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-7x%2B-5+=+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=%28-7%29%5E2-4%2A3%2A-5=109 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-7%29%5E2-4%2A3%2A-5=109\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=109 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+109+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--7%2B-sqrt%28+109+%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-%28-7%29%2Bsqrt%28+109+%29%29%2F2%5C3+=+2.90671775148509 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+109+%29%29%2F2%5C3+=+2.90671775148509\"   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-%28-7%29-sqrt%28+109+%29%29%2F2%5C3+=+-0.573384418151758 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-7%29-sqrt%28+109+%29%29%2F2%5C3+=+-0.573384418151758\"   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-7x%2B-5 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-7x%2B-5\"   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-7x%2B-5+=+%28x-2.90671775148509%29%2A%28x--0.573384418151758%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-7x%2B-5+=+%28x-2.90671775148509%29%2A%28x--0.573384418151758%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.90671775148509, -0.573384418151758.\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-7%2Ax%2B-5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-7%2Ax%2B-5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "-------------------------------<BR>\n" );
document.write( "The other tutor used -3 for the x^2 term.<BR>\n" );
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