document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=532498>Question 532498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the process and answer to the following quadratic equation using the method from India? x2 -2x -13 =0    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350858 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=350858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is no India method or American mehod in Algebra.\r<BR>\n" );
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document.write( "In 8th. Century BC \"Sulbha sutras\" gave an account of how Indian Mathemeticians used Geometry to calculate the roots of the quadratic equation.\r<BR>\n" );
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document.write( "The constant was shifted to the right side of the equation ax^2+bx +c\r<BR>\n" );
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document.write( "ax^2+bx =c\r<BR>\n" );
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document.write( "The you then complete the square on the left side by adding a term . Add the same term on the right side.\r<BR>\n" );
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document.write( "Take the square root on both sides .\r<BR>\n" );
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document.write( "so x will have two values<BR>\n" );
document.write( "This is the method which you are referring to.\r<BR>\n" );
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document.write( "EXAMPLE\r<BR>\n" );
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document.write( "x^2 + 12x -64 =0<BR>\n" );
document.write( "x^2 + 12x = 64<BR>\n" );
document.write( "4x^2 + 48x = 256<BR>\n" );
document.write( "4x^2 + 48x + 144 = 400\r<BR>\n" );
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document.write( "(2x+12)^2 = 4x^2 + 48x + 144 = 400<BR>\n" );
document.write( " solve for x<BR>\n" );
document.write( "2x+12 = 20<BR>\n" );
document.write( "2x = 8<BR>\n" );
document.write( "x = 4<BR>\n" );
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document.write( "2x+12 = -20<BR>\n" );
document.write( "2x = -32<BR>\n" );
document.write( "x = -16<BR>\n" );
document.write( "-----\r<BR>\n" );
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document.write( " ---------price		----------------			quantity								<BR>\n" );
document.write( "Solution I	3	----------------			x	ml							<BR>\n" );
document.write( "Solution II	55	------	130	-	x	ml							<BR>\n" );
document.write( "Mixture	39.00%	----------------	130										<BR>\n" );
document.write( "													<BR>\n" );
document.write( "3	x	+	55	(	130	-	x	)	=	39	*	130	<BR>\n" );
document.write( "													<BR>\n" );
document.write( "3	x	+	7150	-	55	x	=			5070			<BR>\n" );
document.write( "3	x	-	55	x			=	5070	-	7150			<BR>\n" );
document.write( "-52	x			=	-2080								<BR>\n" );
document.write( "/	-52												<BR>\n" );
document.write( "	x			=	40		ml			3.00%		Solution I	<BR>\n" );
document.write( "					90		ml			55.00%		Solution II	\r<BR>\n" );
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document.write( "x^2-2x-13 can be solved by using the quadratic formula or completing the squares method\r<BR>\n" );
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document.write( "Find the roots of the equation by quadratic formula					<BR>\n" );
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document.write( "a=	1	,b=	-2	,c=	-13<BR>\n" );
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document.write( "b^2-4ac=	4	+	52		<BR>\n" );
document.write( "b^2-4ac=	56				<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >					<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >					<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1=%28-12%2B21%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"x1=%28-12%2B21%29%2F%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >					<BR>\n" );
document.write( "x1=(	2	+	7.48	)/	2<BR>\n" );
document.write( "x1=	4.74				<BR>\n" );
document.write( "x2=(	2	-7.48	) /	2	<BR>\n" );
document.write( "x2= 	-2.74				<BR>\n" );
document.write( "The roots are (4.74,-2.74)\r<BR>\n" );
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document.write( "m.ananth@hotmail.ca \r<BR>\n" );
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document.write( " </SPAN>\n" );
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