document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86230>Question 86230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9msquared+11m=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62465 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=62465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9m%5E2+%2B+11m+=+0 ALIGN=MIDDLE  ALT=\"9m%5E2+%2B+11m+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "One of the first things you can notice in the given equation is that all the terms on the <BR>\n" );
document.write( "left side contain the variable \"m\".  You can factor it out and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2A%289m+%2B+11%29+=+0 ALIGN=MIDDLE  ALT=\"m%2A%289m+%2B+11%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice now that the left side has two factors that multiply each other.  If either of these<BR>\n" );
document.write( "factors is equal to zero, the left side of the equation will have one factor multiplied<BR>\n" );
document.write( "by zero.  Therefore, the left side will equal the right side.<BR>\n" );
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document.write( "So we have two possible solutions to this equation. Either m = 0 or the other factor<BR>\n" );
document.write( "(9m + 11) equals zero.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+0 ALIGN=MIDDLE  ALT=\"m+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one solution.  The other solution we get by setting 9m + 11 equal to zero:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9m+%2B+11+=+0 ALIGN=MIDDLE  ALT=\"9m+%2B+11+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 11 from both sides of the equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9m+=+-11 ALIGN=MIDDLE  ALT=\"9m+=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, divide both sides of this equation by 9, the multiplier of x, and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9m%2F9+=+%28-11%29%2F9 ALIGN=MIDDLE  ALT=\"9m%2F9+=+%28-11%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-11%29%2F9 ALIGN=MIDDLE  ALT=\"m+=+%28-11%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the two answers to this problem are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+0 ALIGN=MIDDLE  ALT=\"m+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-11%29%2F9 ALIGN=MIDDLE  ALT=\"m+=+%28-11%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand one way (factoring) of solving quadratic equations<BR>\n" );
document.write( "(equations where the highest power of the variable is 2).<BR>\n" );
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