document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473045>Question 473045</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What do you think are some downfalls or potential easy mistakes when using the quadratic formula?\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 #324358 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Quadratic Formula is the method for solving quadratic equations that always work.  Not only that, but if you can remember the formula it’s a fairly simple process as well.\r<BR>\n" );
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document.write( "The important part here is to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=make ALIGN=MIDDLE  ALT=\"make\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sure ALIGN=MIDDLE  ALT=\"+sure\"   DISABLED_style= \"max-width:90%; height:auto;\" > that before we start using the quadratic formula that we have the equation in standard form first.\r<BR>\n" );
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document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B-x%2B-c=0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B-x%2B-c=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "At this point we <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=can ALIGN=MIDDLE  ALT=\"can\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+identify ALIGN=MIDDLE  ALT=\"+identify\"   DISABLED_style= \"max-width:90%; height:auto;\" > the values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > for use in the quadratic formula.  It is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=important ALIGN=MIDDLE  ALT=\"important\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=make ALIGN=MIDDLE  ALT=\"make\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sure ALIGN=MIDDLE  ALT=\"+sure\"   DISABLED_style= \"max-width:90%; height:auto;\" >that we carry any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=minus ALIGN=MIDDLE  ALT=\"minus\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+signs ALIGN=MIDDLE  ALT=\"+signs\"   DISABLED_style= \"max-width:90%; height:auto;\" > along with the constants.\r<BR>\n" );
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document.write( "There is also some simplification that we can do.  We need to be careful however.  One of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=larger ALIGN=MIDDLE  ALT=\"larger\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+mistakes ALIGN=MIDDLE  ALT=\"+mistakes\"   DISABLED_style= \"max-width:90%; height:auto;\" > in this  example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%2B-sqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%282%2B-sqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is to “<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cancel ALIGN=MIDDLE  ALT=\"cancel\"   DISABLED_style= \"max-width:90%; height:auto;\" >” to 2’s in the numerator and denominator.  Remember that in order to cancel anything from the numerator or denominator then it must be multiplied by the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=whole ALIGN=MIDDLE  ALT=\"whole\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+numerator ALIGN=MIDDLE  ALT=\"+numerator\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=denominator ALIGN=MIDDLE  ALT=\"denominator\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since the 2 in the numerator isn’t multiplied by the whole denominator it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=can%92t ALIGN=MIDDLE  ALT=\"can%92t\"   DISABLED_style= \"max-width:90%; height:auto;\" > be canceled.\r<BR>\n" );
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document.write( "-don’t forget to convert square roots of negative numbers into complex numbers.  Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=when ALIGN=MIDDLE  ALT=\"when\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b ALIGN=MIDDLE  ALT=\"+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" > be very careful with the substitution.  This is particularly true for the squared portion under the radical.  Remember that when you square a negative number it will become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  One of the more common mistakes here is to get in a hurry and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=forget ALIGN=MIDDLE  ALT=\"forget\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drop ALIGN=MIDDLE  ALT=\"drop\"   DISABLED_style= \"max-width:90%; height:auto;\" > the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=minus ALIGN=MIDDLE  ALT=\"minus\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sign ALIGN=MIDDLE  ALT=\"+sign\"   DISABLED_style= \"max-width:90%; height:auto;\" > after you square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so be careful.\r<BR>\n" );
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