document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75656>Question 75656</A>: <I><SPAN STYLE=\"word-break: break-all;\">      _5___+__46____=2<BR>\n" );
document.write( "    2x+6     7x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54339 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%282x%2B6%29%2B46%2F%287x%29=2 ALIGN=MIDDLE  ALT=\"5%2F%282x%2B6%29%2B46%2F%287x%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x%282x%2B6%29%29%285%2Fcross%282x%2B6%29%2B46%2Fcross%287x%29%29=2%2A%287x%282x%2B6%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD (which is 7x(2x+6)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A7x%2B46%282x%2B6%29=14x%282x%2B6%29 ALIGN=MIDDLE  ALT=\"5%2A7x%2B46%282x%2B6%29=14x%282x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35x%2B92x%2B276=28x%5E2%2B84x ALIGN=MIDDLE  ALT=\"35x%2B92x%2B276=28x%5E2%2B84x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the 46 on the left and distribute the 7x on the right<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=127x%2B276=28x%5E2%2B84x ALIGN=MIDDLE  ALT=\"127x%2B276=28x%5E2%2B84x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=28x%5E2%2B84x-127x-276 ALIGN=MIDDLE  ALT=\"0=28x%5E2%2B84x-127x-276\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to one side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=28x%5E2-43x-276 ALIGN=MIDDLE  ALT=\"0=28x%5E2-43x-276\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms and simplify. Now use the quadratic formula to solve for x:\r<BR>\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=quadratic.solver>SOLVE quadratic equation with variable</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=28x%5E2%2B-43x%2B-276+=+0 ALIGN=MIDDLE  ALT=\"28x%5E2%2B-43x%2B-276+=+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=%28-43%29%5E2-4%2A28%2A-276=32761 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-43%29%5E2-4%2A28%2A-276=32761\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=32761 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--43%2B-sqrt%28+32761+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--43%2B-sqrt%28+32761+%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-%28-43%29%2Bsqrt%28+32761+%29%29%2F2%5C28+=+4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-43%29%2Bsqrt%28+32761+%29%29%2F2%5C28+=+4\"   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-%28-43%29-sqrt%28+32761+%29%29%2F2%5C28+=+-2.46428571428571 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-43%29-sqrt%28+32761+%29%29%2F2%5C28+=+-2.46428571428571\"   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=28x%5E2%2B-43x%2B-276 ALIGN=MIDDLE  ALT=\"28x%5E2%2B-43x%2B-276\"   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=28x%5E2%2B-43x%2B-276+=+28%28x-4%29%2A%28x--2.46428571428571%29 ALIGN=MIDDLE  ALT=\"28x%5E2%2B-43x%2B-276+=+28%28x-4%29%2A%28x--2.46428571428571%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4, -2.46428571428571.\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+28%2Ax%5E2%2B-43%2Ax%2B-276+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+28%2Ax%5E2%2B-43%2Ax%2B-276+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "So x=-2.4642857 and x=4 </SPAN>\n" );
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