document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=648116>Question 648116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4x squared-4x-99=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406564 by </B><A HREF=/tutors/aboutme.mpl?userid=Algebraic><B>Algebraic(50)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Algebraic><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=Algebraic><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=406564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Original problem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-4x-99 ALIGN=MIDDLE  ALT=\"4x%5E2-4x-99\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We're going to be factoring this to extract the roots (what 'x' equals)\r<BR>\n" );
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document.write( "Step 1: We must find two numbers that when '4' and '-99' multiply, will divide to give you '-4' in the middle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-4x-99 ALIGN=MIDDLE  ALT=\"4x%5E2-4x-99\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You have quite a few number of combinations:\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2 ALIGN=MIDDLE  ALT=\"4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be broken up into\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x++%29%28x++%29 ALIGN=MIDDLE  ALT=\"%284x++%29%28x++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x++%29%282x++%29 ALIGN=MIDDLE  ALT=\"%282x++%29%282x++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We know that '-99' has six factors, and these include:\r<BR>\n" );
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document.write( "1 x 99, 3 x 33, and 9 x 11\r<BR>\n" );
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document.write( "Step 2: Let's start trying to see what will work and not work (trial and error method)\r<BR>\n" );
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document.write( "We know that regardless of signs, none of the factors of '-99' will be able to multiply here to give you a '-4' in the middle using this equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+%2B+3+%29%28x+-+33+%29 ALIGN=MIDDLE  ALT=\"%284x+%2B+3+%29%28x+-+33+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-33x+%2B+3x ALIGN=MIDDLE  ALT=\"-33x+%2B+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+-+3+%29%28x+%2B+33+%29 ALIGN=MIDDLE  ALT=\"%284x+-+3+%29%28x+%2B+33+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33x+-+3x ALIGN=MIDDLE  ALT=\"33x+-+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+%2B++1+%29%28x+-+99+%29 ALIGN=MIDDLE  ALT=\"%284x+%2B++1+%29%28x+-+99+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-396x+%2B+x ALIGN=MIDDLE  ALT=\"-396x+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+-+1+%29%28x+%2B+99+%29 ALIGN=MIDDLE  ALT=\"%284x+-+1+%29%28x+%2B+99+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=396x+-+x ALIGN=MIDDLE  ALT=\"396x+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+%2B+9+%29%28x+-+11+%29 ALIGN=MIDDLE  ALT=\"%284x+%2B+9+%29%28x+-+11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-44x+%2B+9x ALIGN=MIDDLE  ALT=\"-44x+%2B+9x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+-+9+%29%28x+%2B+11+%29 ALIGN=MIDDLE  ALT=\"%284x+-+9+%29%28x+%2B+11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44x+-+9x ALIGN=MIDDLE  ALT=\"44x+-+9x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle\r<BR>\n" );
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document.write( "Now that we know that the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x++%29%28x++%29 ALIGN=MIDDLE  ALT=\"%284x++%29%28x++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equation won't work, let's move on to the other equation that could possibly work..\r<BR>\n" );
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document.write( "Step 3: Let's start trying to see what will work and not work (trial and error method)\r<BR>\n" );
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document.write( "We know that '-99' has six factors, and these include:\r<BR>\n" );
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document.write( "1 x 99, 3 x 33, and 9 x 11\r<BR>\n" );
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document.write( "We know that regardless of signs, none of the factors of '-99' will be able to multiply here to give you a '-4' in the middle using this equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+1+%29%282x+-+99+%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+1+%29%282x+-+99+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-198x+%2B+2x ALIGN=MIDDLE  ALT=\"-198x+%2B+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+1+%29%282x+%2B+99+%29 ALIGN=MIDDLE  ALT=\"%282x+-+1+%29%282x+%2B+99+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=198x+-+2x ALIGN=MIDDLE  ALT=\"198x+-+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+3+%29%282x+-+33+%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+3+%29%282x+-+33+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-66x+%2B+6x ALIGN=MIDDLE  ALT=\"-66x+%2B+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+3+%29%282x+%2B+33+%29 ALIGN=MIDDLE  ALT=\"%282x+-+3+%29%282x+%2B+33+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66x+-+6x ALIGN=MIDDLE  ALT=\"66x+-+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+9+%29%282x+-+11+%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+9+%29%282x+-+11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --->  Works!!  Gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-22x+%2B+18x ALIGN=MIDDLE  ALT=\"-22x+%2B+18x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle, which is equivalent to '-4x'<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+9+%29%282x+%2B+11+%29 ALIGN=MIDDLE  ALT=\"%282x+-+9+%29%282x+%2B+11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Does not work, gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22x+-+18x ALIGN=MIDDLE  ALT=\"22x+-+18x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the middle\r<BR>\n" );
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document.write( "So.. now we know that the factored version of the equation you provided is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+9+%29%282x+-+11+%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+9+%29%282x+-+11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To get the roots, you must set each parenthesis equal to zero like so..\r<BR>\n" );
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document.write( "Step 1: Set each parenthesis equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+9+%29=0 ALIGN=MIDDLE  ALT=\"%282x+%2B+9+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+11+%29=0 ALIGN=MIDDLE  ALT=\"%282x+-+11+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2: Let's solve each one at a time\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+9+%29=0 ALIGN=MIDDLE  ALT=\"%282x+%2B+9+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract '9' from both sides to get the '2x' by itself\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+9+%29=0 ALIGN=MIDDLE  ALT=\"%282x+%2B+9+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-9 ALIGN=MIDDLE  ALT=\"2x=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by '2' to get 'x' by itself\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-9 ALIGN=MIDDLE  ALT=\"2x=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-9%2F2%29 ALIGN=MIDDLE  ALT=\"x=%28-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First root is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-9%2F2%29 ALIGN=MIDDLE  ALT=\"x=%28-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3: Let's find the other root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+11+%29=0 ALIGN=MIDDLE  ALT=\"%282x+-+11+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add '11' to both sides to get the '2x' by itself\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+11+%29=0 ALIGN=MIDDLE  ALT=\"%282x+-+11+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=11 ALIGN=MIDDLE  ALT=\"2x=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by '2' to get the 'x' by itself\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=11 ALIGN=MIDDLE  ALT=\"2x=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2811%2F2%29 ALIGN=MIDDLE  ALT=\"x=%2811%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Second root is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2811%2F2%29 ALIGN=MIDDLE  ALT=\"x=%2811%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the factored version of this equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+9+%29%282x+-+11+%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+9+%29%282x+-+11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and its roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-9%2F2%29 ALIGN=MIDDLE  ALT=\"x=%28-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2811%2F2%29 ALIGN=MIDDLE  ALT=\"x=%2811%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );