document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170395>Question 170395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: 2x= 5x+9. The 5x+9 is in a square root. \r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125801 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=125801\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help,<BR>\n" );
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document.write( "Please help me solve this equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x=sqrt%28+5x%2B9%29+ ALIGN=MIDDLE  ALT=\"+2x=sqrt%28+5x%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The 5x+9 is in a square root. <BR>\n" );
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document.write( "Thank you<BR>\n" );
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document.write( "To get rid of the square root sign(radical sign), you square both sides<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x=sqrt%28+5x%2B9%29+ ALIGN=MIDDLE  ALT=\"+2x=sqrt%28+5x%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282x%29%5E2=%28sqrt%28+5x%2B9%29%29%5E2+ ALIGN=MIDDLE  ALT=\"+%282x%29%5E2=%28sqrt%28+5x%2B9%29%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, when you square a number in a square root, it will always be the number inside the sign<BR>\n" );
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document.write( "Ex.  (  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sqrt%2825%29%29%5E2+ ALIGN=MIDDLE  ALT=\"+%28sqrt%2825%29%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sqrt%2825%29%29%28sqrt%2825%29%29+ ALIGN=MIDDLE  ALT=\"+%28sqrt%2825%29%29%28sqrt%2825%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%29%285%29+ ALIGN=MIDDLE  ALT=\"+%285%29%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25+ ALIGN=MIDDLE  ALT=\"+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So, for our problem, the radical sign disappears if we square both sides<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282x%29%5E2=%28sqrt%28+5x%2B9%29%29%5E2+ ALIGN=MIDDLE  ALT=\"+%282x%29%5E2=%28sqrt%28+5x%2B9%29%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2=+5x%2B9+ ALIGN=MIDDLE  ALT=\"+4x%5E2=+5x%2B9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we need to move \"5x+9\" to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2=+5x%2B9+ ALIGN=MIDDLE  ALT=\"+4x%5E2=+5x%2B9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-5x-9=+5x-5x%2B9-9+ ALIGN=MIDDLE  ALT=\"+4x%5E2-5x-9=+5x-5x%2B9-9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-5x-9=+0+ ALIGN=MIDDLE  ALT=\"+4x%5E2-5x-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is a quadratic equation<BR>\n" );
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document.write( "Quadratic equations are in the form <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;\" >, We can solve this equation by using the quadratic equation<BR>\n" );
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document.write( "Quadratic equation = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"++%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-5x-9=+0+ ALIGN=MIDDLE  ALT=\"+4x%5E2-5x-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<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;\" ><BR>\n" );
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document.write( "For our equation<BR>\n" );
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document.write( "a = 4<BR>\n" );
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document.write( "b = (-5)<BR>\n" );
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document.write( "c = (-9)<BR>\n" );
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document.write( "Now replace the letters with these numbers in the equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"++%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A%284%29%2A%28-9%29+%29%29%2F%282%2A%284%29%29+ ALIGN=MIDDLE  ALT=\"++%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A%284%29%2A%28-9%29+%29%29%2F%282%2A%284%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%285+%2B-+sqrt%28+25-%28-144%29+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"++%285+%2B-+sqrt%28+25-%28-144%29+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%285+%2B-+sqrt%28+25%2B144+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"++%285+%2B-+sqrt%28+25%2B144+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%285+%2B-+sqrt%28+169+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"++%285+%2B-+sqrt%28+169+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%285+%2B-+13%29%2F8+ ALIGN=MIDDLE  ALT=\"++%285+%2B-+13%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=++%285+%2B+13%29%2F8+ ALIGN=MIDDLE  ALT=\"+x+=++%285+%2B+13%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+18%2F8+ ALIGN=MIDDLE  ALT=\"+x+=+18%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+9%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=++%285+-+13%29%2F8+ ALIGN=MIDDLE  ALT=\"+x+=++%285+-+13%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=++-8%2F8+ ALIGN=MIDDLE  ALT=\"+x+=++-8%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+9%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can check by replacing \"x\" with these two numbers in the original quadratic equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+9%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-5x-9=+0+ ALIGN=MIDDLE  ALT=\"+4x%5E2-5x-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%289%2F4%29%5E2-5%289%2F4%29-9=+0+ ALIGN=MIDDLE  ALT=\"+4%289%2F4%29%5E2-5%289%2F4%29-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284%2F1%29%2881%2F16%29-%285%2F1%29%289%2F4%29-9=+0+ ALIGN=MIDDLE  ALT=\"+%284%2F1%29%2881%2F16%29-%285%2F1%29%289%2F4%29-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28324%2F16%29-%2845%2F4%29-9=+0+ ALIGN=MIDDLE  ALT=\"+%28324%2F16%29-%2845%2F4%29-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2881%2F4%29-%2845%2F4%29-9=+0+ ALIGN=MIDDLE  ALT=\"+%2881%2F4%29-%2845%2F4%29-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2836%2F4%29-9=+0+ ALIGN=MIDDLE  ALT=\"+%2836%2F4%29-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9+-+9+=+0+ ALIGN=MIDDLE  ALT=\"+9+-+9+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-5x-9=+0+ ALIGN=MIDDLE  ALT=\"+4x%5E2-5x-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%28-1%29%5E2-5%28-1%29-9=+0+ ALIGN=MIDDLE  ALT=\"+4%28-1%29%5E2-5%28-1%29-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%281%29-%28-5%29-9=+0+ ALIGN=MIDDLE  ALT=\"+4%281%29-%28-5%29-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2B5-9=+0+ ALIGN=MIDDLE  ALT=\"+4%2B5-9=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9+-+9+=+0+ ALIGN=MIDDLE  ALT=\"+9+-+9+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "Since this was not our very first original equation, we have to make sure that the number inside the radical, is not negative, and make sure that the statement is correct<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+9%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x=sqrt%28+5x%2B9%29+ ALIGN=MIDDLE  ALT=\"+2x=sqrt%28+5x%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%289%2F4%29=sqrt%28+5%289%2F4%29%2B9%29+ ALIGN=MIDDLE  ALT=\"+2%289%2F4%29=sqrt%28+5%289%2F4%29%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18%2F4=sqrt%28+%2845%2F4%29%2B9%29+ ALIGN=MIDDLE  ALT=\"+18%2F4=sqrt%28+%2845%2F4%29%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%2F2=sqrt%28+%2845%2F4%29%2B%2836%2F4%29%29+ ALIGN=MIDDLE  ALT=\"+9%2F2=sqrt%28+%2845%2F4%29%2B%2836%2F4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%2F2=sqrt%28+%2881%2F4%29%29+ ALIGN=MIDDLE  ALT=\"+9%2F2=sqrt%28+%2881%2F4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%2F2=9%2F2+ ALIGN=MIDDLE  ALT=\"+9%2F2=9%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x=sqrt%28+5x%2B9%29+ ALIGN=MIDDLE  ALT=\"+2x=sqrt%28+5x%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28-1%29=sqrt%28+5%28-1%29%2B9%29+ ALIGN=MIDDLE  ALT=\"+2%28-1%29=sqrt%28+5%28-1%29%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2%29=sqrt%28+%28-5%29%2B9%29+ ALIGN=MIDDLE  ALT=\"+%28-2%29=sqrt%28+%28-5%29%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2%29=sqrt%28+4%29+ ALIGN=MIDDLE  ALT=\"+%28-2%29=sqrt%28+4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2%29+=+2+ ALIGN=MIDDLE  ALT=\"+%28-2%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (False), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not an answer<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+%28300%2C300%2C-10%2C10%2C-10%2C10%2C+2x+-+sqrt%28+5x%2B9%29%29+ ALIGN=MIDDLE  ALT=\"+graph+%28300%2C300%2C-10%2C10%2C-10%2C10%2C+2x+-+sqrt%28+5x%2B9%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The line only crosses at one point on the x axis, at point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F4 ALIGN=MIDDLE  ALT=\"9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+9%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is your answer<BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
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