document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206468>Question 1206468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find x,<BR>\n" );
document.write( "x + √{(x - ½) + √(x + ¼)} = 1024 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844015 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=844015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+sqrt%28%28x+-+1%2F2%29+%2B+sqrt%28x+%2B+1%2F4%29%29+=+1024 ALIGN=MIDDLE  ALT=\"x+%2B+sqrt%28%28x+-+1%2F2%29+%2B+sqrt%28x+%2B+1%2F4%29%29+=+1024\"   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=sqrt%28%28x+-+1%2F2%29+%2B+sqrt%28x+%2B+1%2F4%29%29+=+1024-x ALIGN=MIDDLE  ALT=\"sqrt%28%28x+-+1%2F2%29+%2B+sqrt%28x+%2B+1%2F4%29%29+=+1024-x\"   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=%28sqrt%28%28x+-+1%2F2%29+%2B+sqrt%28x+%2B+1%2F4%29%29%29%5E2+=+%281024-x%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28%28x+-+1%2F2%29+%2B+sqrt%28x+%2B+1%2F4%29%29%29%5E2+=+%281024-x%29%5E2\"   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+-+1%2F2+%2B+sqrt%28x+%2B+1%2F4%29+=x%5E2+-+2048+x+%2B+1048576 ALIGN=MIDDLE  ALT=\"x+-+1%2F2+%2B+sqrt%28x+%2B+1%2F4%29+=x%5E2+-+2048+x+%2B+1048576\"   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=sqrt%28x+%2B+1%2F4%29+=x%5E2+-+2048x+-x%2B+1048576%2B1%2F2 ALIGN=MIDDLE  ALT=\"sqrt%28x+%2B+1%2F4%29+=x%5E2+-+2048x+-x%2B+1048576%2B1%2F2\"   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=%28sqrt%28x+%2B+1%2F4%29%29%5E2+=%28x%5E2+-+2049+x+%2B+2097153%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28x+%2B+1%2F4%29%29%5E2+=%28x%5E2+-+2049+x+%2B+2097153%2F2%29%5E2\"   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+%2B+1%2F4=x%5E4+-+4098+x%5E3+%2B+6295554+x%5E2+-+4297066497+x+%2B+4398050705409%2F4 ALIGN=MIDDLE  ALT=\"x+%2B+1%2F4=x%5E4+-+4098+x%5E3+%2B+6295554+x%5E2+-+4297066497+x+%2B+4398050705409%2F4\"   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%5E4+-+4098+x%5E3+%2B+6295554x%5E2+-+4297066497x+%2B+4398050705409%2F4-x-1%2F4=0 ALIGN=MIDDLE  ALT=\"x%5E4+-+4098+x%5E3+%2B+6295554x%5E2+-+4297066497x+%2B+4398050705409%2F4-x-1%2F4=0\"   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%5E4+-+4098+x%5E3+%2B+6295554x%5E2+-+4297066498x+%2B1099512676352+=0 ALIGN=MIDDLE  ALT=\"x%5E4+-+4098+x%5E3+%2B+6295554x%5E2+-+4297066498x+%2B1099512676352+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using calculator we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=992.02 ALIGN=MIDDLE  ALT=\"x=992.02\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=993 ALIGN=MIDDLE  ALT=\"x=993\"   DISABLED_style= \"max-width:90%; height:auto;\" >= >will not work (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1025%3E1024 ALIGN=MIDDLE  ALT=\"1025%3E1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%E2%89%881056.0+ ALIGN=MIDDLE  ALT=\"x%E2%89%881056.0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= >will not work (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1056%3E1024 ALIGN=MIDDLE  ALT=\"1056%3E1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1057 ALIGN=MIDDLE  ALT=\"x=1057\"   DISABLED_style= \"max-width:90%; height:auto;\" >= >will not work (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1057%3E1024 ALIGN=MIDDLE  ALT=\"1057%3E1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " verifying solutions shows that only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=992.02 ALIGN=MIDDLE  ALT=\"x=992.02\"   DISABLED_style= \"max-width:90%; height:auto;\" > works\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=992.02+%2B+sqrt%28%28992.02+-+1%2F2%29+%2B+sqrt%28992.02+%2B+1%2F4%29%29=1024 ALIGN=MIDDLE  ALT=\"992.02+%2B+sqrt%28%28992.02+-+1%2F2%29+%2B+sqrt%28992.02+%2B+1%2F4%29%29=1024\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>true\r<BR>\n" );
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document.write( "so, answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=992.02 ALIGN=MIDDLE  ALT=\"x=992.02\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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