document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162005>Question 162005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> pls.help me solve the following quadratic equation by factoring:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-3x%2B1=0 ALIGN=MIDDLE  ALT=\"2x%5E2-3x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B9x=9 ALIGN=MIDDLE  ALT=\"4x%5E2%2B9x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2%2By=-11y ALIGN=MIDDLE  ALT=\"2y%5E2%2By=-11y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-7-44=0 ALIGN=MIDDLE  ALT=\"y%5E2-7-44=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B11x-1=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B11x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "pls. submit your answer as soon as possible i need to pass it tomorrow<BR>\n" );
document.write( "im begging you pls.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119394 by </B><A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><B>KnightOwlTutor(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><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=KnightOwlTutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=119394\">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=2x%5E2-3x%2B1=0 ALIGN=MIDDLE  ALT=\"2x%5E2-3x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We know that the last term must be 1\r<BR>\n" );
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document.write( "Set up the equation like this<BR>\n" );
document.write( "it could be -1,-1 or 1,1\r<BR>\n" );
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document.write( "Because you have a negative middle term it is most likely -1,-1\r<BR>\n" );
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document.write( "(2x-1)(x-1)=0\r<BR>\n" );
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document.write( "Therefore the solution is x= 1/2 or 1 we need to make the equation=0 and the only way to accomplish this is to make one or both terms =0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B9x=9 ALIGN=MIDDLE  ALT=\"4x%5E2%2B9x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We need to subtract 9 from both sides of the equation \r<BR>\n" );
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document.write( "4x^2+9x-9=0\r<BR>\n" );
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document.write( "We need to find two numbers that have a product of 9 the possibilities are 3,3<BR>\n" );
document.write( "9,1<BR>\n" );
document.write( "We have a negative number so we know that the product is -\r<BR>\n" );
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document.write( "We then need to know what 2 numbers give a product of 4\r<BR>\n" );
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document.write( "2,2 or 4,1\r<BR>\n" );
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document.write( "Let's set up the equation\r<BR>\n" );
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document.write( "using 3,3\r<BR>\n" );
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document.write( "(_x-3)(_x+3)<BR>\n" );
document.write( "The middle terms need to add up to 9x Let's try 4 and 1\r<BR>\n" );
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document.write( "(4x-3)(x+3)  The middle term for this problem is -3x+12x=9x\r<BR>\n" );
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document.write( "We have the correct factors<BR>\n" );
document.write( "the solution is x=3/4 or -3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2%2By=-11y ALIGN=MIDDLE  ALT=\"2y%5E2%2By=-11y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here we add 11y to both sides of the equation\r<BR>\n" );
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document.write( "2y^2+y+11y=0\r<BR>\n" );
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document.write( "2y^2+12y=0\r<BR>\n" );
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document.write( "factor out 2<BR>\n" );
document.write( "2(y^2+6)=0<BR>\n" );
document.write( "y=sqrt6 i<BR>\n" );
document.write( "remember that i=sqrt of -1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-7-44=0 ALIGN=MIDDLE  ALT=\"y%5E2-7-44=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First we try to calculate the numbers that generate a product of 44\r<BR>\n" );
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document.write( "4,11 or 44,1\r<BR>\n" );
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document.write( "Let's try 4,11\r<BR>\n" );
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document.write( "(y-11)(y+4)\r<BR>\n" );
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document.write( "y =11 or -4\r<BR>\n" );
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document.write( "6x^2+11x-1=0<BR>\n" );
document.write( "ax^2+bx+c=0 a=6 b=11 c=-1<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=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=6x%5E2%2B11x%2B-1+=+0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B11x%2B-1+=+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=%2811%29%5E2-4%2A6%2A-1=145 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2811%29%5E2-4%2A6%2A-1=145\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=145 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+=+%28-11%2B-sqrt%28+145+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-11%2B-sqrt%28+145+%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-%2811%29%2Bsqrt%28+145+%29%29%2F2%5C6+=+0.0867995482326913 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+145+%29%29%2F2%5C6+=+0.0867995482326913\"   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-%2811%29-sqrt%28+145+%29%29%2F2%5C6+=+-1.92013288156602 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2811%29-sqrt%28+145+%29%29%2F2%5C6+=+-1.92013288156602\"   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=6x%5E2%2B11x%2B-1 ALIGN=MIDDLE  ALT=\"6x%5E2%2B11x%2B-1\"   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=6x%5E2%2B11x%2B-1+=+6%28x-0.0867995482326913%29%2A%28x--1.92013288156602%29 ALIGN=MIDDLE  ALT=\"6x%5E2%2B11x%2B-1+=+6%28x-0.0867995482326913%29%2A%28x--1.92013288156602%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.0867995482326913, -1.92013288156602.\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+6%2Ax%5E2%2B11%2Ax%2B-1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B11%2Ax%2B-1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Use the quadratic formula </SPAN>\n" );
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