document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255158>Question 255158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the solution to the system of equations x^2 - x + 6 = y and 2x + 2y = 36?\r<BR>\n" );
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document.write( "Answer 187449 by richwmiller(1774) About Me  on 2010-01-09 17:12:13:<BR>\n" );
document.write( "You can put this solution on YOUR website!<BR>\n" );
document.write( "x = -2 sqrt(3), y = 2 (9+sqrt(3)) x=-3.4641, y=21.4641<BR>\n" );
document.write( "x = 2 sqrt(3), y = -2 (sqrt(3)-9) x=3.4641, y=14.5359<BR>\n" );
document.write( "It is a line crossing a parabola.  \r<BR>\n" );
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document.write( "Please explain this in detail thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187463 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=187463\">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=x%5E2+-+x+%2B+6+=+y+ ALIGN=MIDDLE  ALT=\"x%5E2+-+x+%2B+6+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-+x+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-+x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2y+=+36 ALIGN=MIDDLE  ALT=\"2x+%2B+2y+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2%28x%5E2+-+x+%2B+6%29+=+36 ALIGN=MIDDLE  ALT=\"2x+%2B+2%28x%5E2+-+x+%2B+6%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-+x+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-+x+%2B+6\"   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+%2B+2x%5E2+-+2x+%2B+12+=+36 ALIGN=MIDDLE  ALT=\"2x+%2B+2x%5E2+-+2x+%2B+12+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2x%5E2-2x%2B12-36=0 ALIGN=MIDDLE  ALT=\"2x%2B2x%5E2-2x%2B12-36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get every term to the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B0x-24=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B0x-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B0x-24 ALIGN=MIDDLE  ALT=\"2x%5E2%2B0x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2 ALIGN=MIDDLE  ALT=\"A=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=0 ALIGN=MIDDLE  ALT=\"B=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-24 ALIGN=MIDDLE  ALT=\"C=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"x\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%280%29+%2B-+sqrt%28+%280%29%5E2-4%282%29%28-24%29+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28%280%29+%2B-+sqrt%28+%280%29%5E2-4%282%29%28-24%29+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2 ALIGN=MIDDLE  ALT=\"A=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=0 ALIGN=MIDDLE  ALT=\"B=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-24 ALIGN=MIDDLE  ALT=\"C=-24\"   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+=+%280+%2B-+sqrt%28+0-4%282%29%28-24%29+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+0-4%282%29%28-24%29+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"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+=+%280+%2B-+sqrt%28+0--192+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+0--192+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%282%29%28-24%29 ALIGN=MIDDLE  ALT=\"4%282%29%28-24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-192 ALIGN=MIDDLE  ALT=\"-192\"   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+=+%280+%2B-+sqrt%28+0%2B192+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+0%2B192+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%280--192%29 ALIGN=MIDDLE  ALT=\"sqrt%280--192%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%280%2B192%29 ALIGN=MIDDLE  ALT=\"sqrt%280%2B192%29\"   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+=+%280+%2B-+sqrt%28+192+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+192+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=192 ALIGN=MIDDLE  ALT=\"192\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=192 ALIGN=MIDDLE  ALT=\"192\"   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+=+%280+%2B-+sqrt%28+192+%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+192+%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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+=+%280+%2B-+8%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+8%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280%29%2F%284%29+%2B-+%288%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%280%29%2F%284%29+%2B-+%288%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%22%22+%2B-+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+%22%22+%2B-+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+-2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "So the solutions in terms of 'x' are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+-2%2Asqrt%283%29\"   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=3.464 ALIGN=MIDDLE  ALT=\"x=3.464\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3.464 ALIGN=MIDDLE  ALT=\"x=-3.464\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now let's find the corresponding solution for y when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=2%2Asqrt%283%29\"   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=y+=+x%5E2+-+x+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-+x+%2B+6\"   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=y+=+%282%2Asqrt%283%29%29%5E2+-+2%2Asqrt%283%29+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+%282%2Asqrt%283%29%29%5E2+-+2%2Asqrt%283%29+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=2%2Asqrt%283%29\"   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=y+=+12+-+2%2Asqrt%283%29+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+12+-+2%2Asqrt%283%29+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%283%29%29%5E2=2%5E2%2A%28sqrt%283%29%29%5E2=4%2A3=12 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%283%29%29%5E2=2%5E2%2A%28sqrt%283%29%29%5E2=4%2A3=12\"   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=y+=+18+-+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+18+-+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+18+-+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+18+-+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=14.536 ALIGN=MIDDLE  ALT=\"y=14.536\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's find the corresponding solution for y when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-2%2Asqrt%283%29\"   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=y+=+x%5E2+-+x+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-+x+%2B+6\"   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=y+=+%28-2%2Asqrt%283%29%29%5E2+%2B+2%2Asqrt%283%29+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+%28-2%2Asqrt%283%29%29%5E2+%2B+2%2Asqrt%283%29+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-2%2Asqrt%283%29\"   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=y+=+12+%2B+2%2Asqrt%283%29+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+12+%2B+2%2Asqrt%283%29+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"-2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2Asqrt%283%29%29%5E2=%28-2%29%5E2%2A%28sqrt%283%29%29%5E2=4%2A3=12 ALIGN=MIDDLE  ALT=\"%28-2%2Asqrt%283%29%29%5E2=%28-2%29%5E2%2A%28sqrt%283%29%29%5E2=4%2A3=12\"   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=y+=+18+%2B+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+18+%2B+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+18+-+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+18+-+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=21.464 ALIGN=MIDDLE  ALT=\"y=21.464\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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