document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246123>Question 246123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the quadratic.  2b(6b+13)=-12\r<BR>\n" );
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document.write( "I get 12b^2+26b+12=0 but not sure what to do next.  May I please ask for assistance in solving this quadratic equation?  Thanks\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179761 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> divide both sides by 12<BR>\n" );
document.write( "12b^2+26b+12=0\r<BR>\n" );
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document.write( "you can solve by factoring, completng the square or by quadratic formula\r<BR>\n" );
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document.write( "You get -3/2 (-1.5) and -2/3 (-.667)<BR>\n" );
document.write( "I like completing the square.<BR>\n" );
document.write( "12b^2+26b=-12<BR>\n" );
document.write( "divide by 12<BR>\n" );
document.write( "b^2+(26/12)(b)=-1\r<BR>\n" );
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document.write( "b^2+(13/6)(b)=-1<BR>\n" );
document.write( "add 1/2*(13/6)^2 =169/144 to both sides<BR>\n" );
document.write( "b^2+(13/6)(b)+169/144=25/144<BR>\n" );
document.write( "factor<BR>\n" );
document.write( "|b+13/12|=-5/12<BR>\n" );
document.write( "b=-5/12-13/12=-18/12=-3/2<BR>\n" );
document.write( "b=+5/12-13/12=-8/12=-2/3<BR>\n" );
document.write( "see below for other methods<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=12x%5E2%2B26x%2B12+=+0 ALIGN=MIDDLE  ALT=\"12x%5E2%2B26x%2B12+=+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=%2826%29%5E2-4%2A12%2A12=100 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2826%29%5E2-4%2A12%2A12=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=100 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+=+%28-26%2B-sqrt%28+100+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-26%2B-sqrt%28+100+%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-%2826%29%2Bsqrt%28+100+%29%29%2F2%5C12+=+-0.666666666666667 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2826%29%2Bsqrt%28+100+%29%29%2F2%5C12+=+-0.666666666666667\"   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-%2826%29-sqrt%28+100+%29%29%2F2%5C12+=+-1.5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2826%29-sqrt%28+100+%29%29%2F2%5C12+=+-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2%2B26x%2B12 ALIGN=MIDDLE  ALT=\"12x%5E2%2B26x%2B12\"   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=12x%5E2%2B26x%2B12+=+12%28x--0.666666666666667%29%2A%28x--1.5%29 ALIGN=MIDDLE  ALT=\"12x%5E2%2B26x%2B12+=+12%28x--0.666666666666667%29%2A%28x--1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.666666666666667, -1.5.\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+12%2Ax%5E2%2B26%2Ax%2B12+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B26%2Ax%2B12+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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