document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148748>Question 148748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not sure if I submitted my last question right.\r<BR>\n" );
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document.write( "The problem is to solve the quadratic equation using the Indian method of multiplying each term in the equation by four times the coefficient of the x sqrt 2 term.<BR>\n" );
document.write( "The equation is  4x^2 - 4x + 3 = 0\r<BR>\n" );
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document.write( "Please help\r<BR>\n" );
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document.write( "Ellen </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109100 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=109100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+4x+%2B+3+=+0+ ALIGN=MIDDLE  ALT=\"4x%5E2+-+4x+%2B+3+=+0+\"   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%5E2+-+x+%2B+3%2F4+=+0+ ALIGN=MIDDLE  ALT=\"x%5E2+-+x+%2B+3%2F4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide everything by the leading coefficient 4. We <font size=4><b>must</b></font> have a leading coefficient of 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+=+-3%2F4+ ALIGN=MIDDLE  ALT=\"x%5E2+-+x+=+-3%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+%2B1%2F4=+-3%2F4%2B1%2F4+ ALIGN=MIDDLE  ALT=\"x%5E2+-+x+%2B1%2F4=+-3%2F4%2B1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take half of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and square it to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Add this to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+4x+%2B1=+-3%2B1+ ALIGN=MIDDLE  ALT=\"4x%5E2+-+4x+%2B1=+-3%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply every term by 4. This will eliminate the denominators.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+4x%2B1+=+-2+ ALIGN=MIDDLE  ALT=\"4x%5E2+-+4x%2B1+=+-2+\"   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=%282x-1%29%5E2+=+-2+ ALIGN=MIDDLE  ALT=\"%282x-1%29%5E2+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+4x%2B1 ALIGN=MIDDLE  ALT=\"4x%5E2+-+4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29%5E2 ALIGN=MIDDLE  ALT=\"%282x-1%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=2x-1+=+0%2B-sqrt%28-2%29+ ALIGN=MIDDLE  ALT=\"2x-1+=+0%2B-sqrt%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides to eliminate the squares.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1+=+sqrt%28-2%29+ ALIGN=MIDDLE  ALT=\"2x-1+=+sqrt%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1+=+-sqrt%28-2%29+ ALIGN=MIDDLE  ALT=\"2x-1+=+-sqrt%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1+=+i%2Asqrt%282%29+ ALIGN=MIDDLE  ALT=\"2x-1+=+i%2Asqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1+=+-i%2Asqrt%282%29+ ALIGN=MIDDLE  ALT=\"2x-1+=+-i%2Asqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=+1%2Bi%2Asqrt%282%29+ ALIGN=MIDDLE  ALT=\"2x=+1%2Bi%2Asqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1+=+1-i%2Asqrt%282%29+ ALIGN=MIDDLE  ALT=\"2x-1+=+1-i%2Asqrt%282%29+\"   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=x=+%281%2Bi%2Asqrt%282%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x=+%281%2Bi%2Asqrt%282%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2Bi%2Asqrt%282%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x=%281%2Bi%2Asqrt%282%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2 to isolate x.\r<BR>\n" );
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document.write( "So our answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+%281%2Bi%2Asqrt%282%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x=+%281%2Bi%2Asqrt%282%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2Bi%2Asqrt%282%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x=%281%2Bi%2Asqrt%282%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.207%2Ai ALIGN=MIDDLE  ALT=\"x=1.207%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.207%2Ai ALIGN=MIDDLE  ALT=\"x=-0.207%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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