document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887857>Question 887857</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Stuck on these quadratic equations!\r<BR>\n" );
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document.write( "Trying to find exact solutions.\r<BR>\n" );
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document.write( "X- 5{sqrt}x -24=0\r<BR>\n" );
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document.write( "{sqrt}(6+2n)-2=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536932 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=536932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  find exact solutions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+-+5sqrt%28x%29+-+24+=+0 ALIGN=MIDDLE  ALT=\"X+-+5sqrt%28x%29+-+24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 5sqrt(x) to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+24%29 ALIGN=MIDDLE  ALT=\"%28x+-+24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5sqrt%28x%29 ALIGN=MIDDLE  ALT=\"5sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+24%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+24%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x ALIGN=MIDDLE  ALT=\"25x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "FOIL (x-24)(x-24)<BR>\n" );
document.write( "x^2 - 48x + 576 = 25x<BR>\n" );
document.write( "x^2 - 48x - 25x + 576 = 0<BR>\n" );
document.write( "x^2 - 73x + 576 = 0<BR>\n" );
document.write( "You can use the quadratic formula to find x, but this will factor to:<BR>\n" );
document.write( "(x-9)(x-64) = 0<BR>\n" );
document.write( "two solutions<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "x = 64<BR>\n" );
document.write( " when a radical is involved, it's very important to try both solutions in the original equation<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+-+5sqrt%289%29+-+24+=+0 ALIGN=MIDDLE  ALT=\"9+-+5sqrt%289%29+-+24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "9 - 15 - 24 does not = 0, not a solution<BR>\n" );
document.write( "\and x = 64<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+-+5sqrt%2864%29+-+24+=+0 ALIGN=MIDDLE  ALT=\"64+-+5sqrt%2864%29+-+24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "64 - 5(8) - 24 = 0; only good solution is x = 64<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%2B2n%29-+2+=+2 ALIGN=MIDDLE  ALT=\"sqrt%286%2B2n%29-+2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 2 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%2B2n%29=+4 ALIGN=MIDDLE  ALT=\"sqrt%286%2B2n%29=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "6 + 2n = 16<BR>\n" );
document.write( "2n = 16 - 6<BR>\n" );
document.write( "2n = 10<BR>\n" );
document.write( "n = 5<BR>\n" );
document.write( ":\"<BR>\n" );
document.write( "Check solution in original equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%2B2%285%29%29-+2+=+2 ALIGN=MIDDLE  ALT=\"sqrt%286%2B2%285%29%29-+2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%29-+2+=+2 ALIGN=MIDDLE  ALT=\"sqrt%2816%29-+2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4 - 2 = 2, a good solution </SPAN>\n" );
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