document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122822>Question 122822</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0130220701/algebrahomeworkh>Prentice Hall Algebra 2 with Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I have an algebra 2 question relating to application of the Quadratic formula.\r<BR>\n" );
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document.write( "The problem is: 2y+3/4y-1=3y-2/3y+2\r<BR>\n" );
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document.write( "I have no idea how to do that using the quadratic formula.\r<BR>\n" );
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document.write( "I appreciate your assistance and thank you in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90167 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=90167\">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=%282y%2B3%29%2F%284y-1%29=%283y-2%29%2F%283y%2B2%29 ALIGN=MIDDLE  ALT=\"%282y%2B3%29%2F%284y-1%29=%283y-2%29%2F%283y%2B2%29\"   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=%282y%2B3%29%283y%2B2%29=%283y-2%29%284y-1%29 ALIGN=MIDDLE  ALT=\"%282y%2B3%29%283y%2B2%29=%283y-2%29%284y-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y%5E2%2B13y%2B6=12y%5E2-11y%2B2 ALIGN=MIDDLE  ALT=\"6y%5E2%2B13y%2B6=12y%5E2-11y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y%5E2%2B13y%2B6-12y%5E2%2B11y-2=0 ALIGN=MIDDLE  ALT=\"6y%5E2%2B13y%2B6-12y%5E2%2B11y-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything 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=-6y%5E2%2B24y%2B4=0 ALIGN=MIDDLE  ALT=\"-6y%5E2%2B24y%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for y:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ay%5E2%2Bby%2Bc=0 ALIGN=MIDDLE  ALT=\"ay%5E2%2Bby%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2Ay%5E2%2B24%2Ay%2B4=0 ALIGN=MIDDLE  ALT=\"-6%2Ay%5E2%2B24%2Ay%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-6 ALIGN=MIDDLE  ALT=\"a=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=24 ALIGN=MIDDLE  ALT=\"b=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=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=y+=+%28-24+%2B-+sqrt%28+%2824%29%5E2-4%2A-6%2A4+%29%29%2F%282%2A-6%29 ALIGN=MIDDLE  ALT=\"y+=+%28-24+%2B-+sqrt%28+%2824%29%5E2-4%2A-6%2A4+%29%29%2F%282%2A-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-6, b=24, and c=4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-24+%2B-+sqrt%28+576-4%2A-6%2A4+%29%29%2F%282%2A-6%29 ALIGN=MIDDLE  ALT=\"y+=+%28-24+%2B-+sqrt%28+576-4%2A-6%2A4+%29%29%2F%282%2A-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 24 to get 576  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-24+%2B-+sqrt%28+576%2B96+%29%29%2F%282%2A-6%29 ALIGN=MIDDLE  ALT=\"y+=+%28-24+%2B-+sqrt%28+576%2B96+%29%29%2F%282%2A-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A4%2A-6 ALIGN=MIDDLE  ALT=\"-4%2A4%2A-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96 ALIGN=MIDDLE  ALT=\"96\"   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+=+%28-24+%2B-+sqrt%28+672+%29%29%2F%282%2A-6%29 ALIGN=MIDDLE  ALT=\"y+=+%28-24+%2B-+sqrt%28+672+%29%29%2F%282%2A-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-24+%2B-+4%2Asqrt%2842%29%29%2F%282%2A-6%29 ALIGN=MIDDLE  ALT=\"y+=+%28-24+%2B-+4%2Asqrt%2842%29%29%2F%282%2A-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, 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=y+=+%28-24+%2B-+4%2Asqrt%2842%29%29%2F-12 ALIGN=MIDDLE  ALT=\"y+=+%28-24+%2B-+4%2Asqrt%2842%29%29%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -6 to get -12\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-24+%2B+4%2Asqrt%2842%29%29%2F-12 ALIGN=MIDDLE  ALT=\"y+=+%28-24+%2B+4%2Asqrt%2842%29%29%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-24+-+4%2Asqrt%2842%29%29%2F-12 ALIGN=MIDDLE  ALT=\"y+=+%28-24+-+4%2Asqrt%2842%29%29%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now 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=y=-24%2F-12%2B4%2Asqrt%2842%29%2F-12 ALIGN=MIDDLE  ALT=\"y=-24%2F-12%2B4%2Asqrt%2842%29%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-24%2F-12-4%2Asqrt%2842%29%2F-12 ALIGN=MIDDLE  ALT=\"y=-24%2F-12-4%2Asqrt%2842%29%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2-sqrt%2842%29%2F3 ALIGN=MIDDLE  ALT=\"y=2-sqrt%2842%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Bsqrt%2842%29%2F3 ALIGN=MIDDLE  ALT=\"y=2%2Bsqrt%2842%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.160246899469287 ALIGN=MIDDLE  ALT=\"y=-0.160246899469287\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4.16024689946929 ALIGN=MIDDLE  ALT=\"y=4.16024689946929\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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