document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120366>Question 120366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 3+2i is a solution for x^2+mx+n=0, where m and n are real numbers, what is the value of m? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88232 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=88232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B2i ALIGN=MIDDLE  ALT=\"3%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a solution, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2B2i ALIGN=MIDDLE  ALT=\"x=3%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2B2i ALIGN=MIDDLE  ALT=\"x=3%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=2i ALIGN=MIDDLE  ALT=\"x-3=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F2=i ALIGN=MIDDLE  ALT=\"%28x-3%29%2F2=i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2 to isolate \"i\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F2=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F2=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace i with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%2F2%29%5E2=-1 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%2F2%29%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2F2%5E2=-1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2F2%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the exponent\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2F4=-1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2F4=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 2 to get 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%28x-3%29%5E2=-1 ALIGN=MIDDLE  ALT=\"%281%2F4%29%28x-3%29%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%28x-3%29%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"%281%2F4%29%28x-3%29%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%28x%5E2-6x%2B9%29%2B1=0 ALIGN=MIDDLE  ALT=\"%281%2F4%29%28x%5E2-6x%2B9%29%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x%5E2-%283%2F2%29x%2B9%2F4%2B1=0 ALIGN=MIDDLE  ALT=\"%281%2F4%29x%5E2-%283%2F2%29x%2B9%2F4%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x%5E2-%283%2F2%29x%2B13%2F4=0 ALIGN=MIDDLE  ALT=\"%281%2F4%29x%5E2-%283%2F2%29x%2B13%2F4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28%281%2F4%29x%5E2-%283%2F2%29x%2B13%2F4%29=0 ALIGN=MIDDLE  ALT=\"4%28%281%2F4%29x%5E2-%283%2F2%29x%2B13%2F4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 4 to eliminate any fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B13=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B13=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute. Notice how the fractions have been eliminated.\r<BR>\n" );
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document.write( "So the quadratic that has the solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B2i ALIGN=MIDDLE  ALT=\"3%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-6x%2B13 ALIGN=MIDDLE  ALT=\"y=x%5E2-6x%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since m is the coefficient for the x term in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bmx%2Bn=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bmx%2Bn=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mx=-6x ALIGN=MIDDLE  ALT=\"mx=-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-6 ALIGN=MIDDLE  ALT=\"m=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer: \r<BR>\n" );
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document.write( "So the value of m is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-6 ALIGN=MIDDLE  ALT=\"m=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "You can check your answer by using the quadratic formula </SPAN>\n" );
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