document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=353963>Question 353963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm a little confused on how to work this one...\r<BR>\n" );
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document.write( "4x^4 - 12x^2 - 19 = 0\r<BR>\n" );
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document.write( "I use subtitution of y = x^2 giving me\r<BR>\n" );
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document.write( "4y^2 - 12y - 19 = 0\r<BR>\n" );
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document.write( "My answers are y = 4.145751311 and -1.145751311\r<BR>\n" );
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document.write( "Now I'm not sure what to do from here.\r<BR>\n" );
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document.write( "Thanks a lot for your help!\r<BR>\n" );
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document.write( "Neil </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #253008 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=253008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2+-+12y+-+19+=+0+ ALIGN=MIDDLE  ALT=\"4y%5E2+-+12y+-+19+=+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=4y%5E2-12y-19=0 ALIGN=MIDDLE  ALT=\"4y%5E2-12y-19=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\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=4y%5E2-12y-19 ALIGN=MIDDLE  ALT=\"4y%5E2-12y-19\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ay%5E2%2BBy%2BC ALIGN=MIDDLE  ALT=\"Ay%5E2%2BBy%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-12 ALIGN=MIDDLE  ALT=\"B=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-19 ALIGN=MIDDLE  ALT=\"C=-19\"   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 \"y\":\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%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"y+=+%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=y+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%284%29%28-19%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%284%29%28-19%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-12 ALIGN=MIDDLE  ALT=\"B=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-19 ALIGN=MIDDLE  ALT=\"C=-19\"   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+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%284%29%28-19%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"y+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%284%29%28-19%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"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+=+%2812+%2B-+sqrt%28+144-4%284%29%28-19%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"y+=+%2812+%2B-+sqrt%28+144-4%284%29%28-19%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   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+=+%2812+%2B-+sqrt%28+144--304+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"y+=+%2812+%2B-+sqrt%28+144--304+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%284%29%28-19%29 ALIGN=MIDDLE  ALT=\"4%284%29%28-19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-304 ALIGN=MIDDLE  ALT=\"-304\"   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+=+%2812+%2B-+sqrt%28+144%2B304+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"y+=+%2812+%2B-+sqrt%28+144%2B304+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144--304%29 ALIGN=MIDDLE  ALT=\"sqrt%28144--304%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144%2B304%29 ALIGN=MIDDLE  ALT=\"sqrt%28144%2B304%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+=+%2812+%2B-+sqrt%28+448+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"y+=+%2812+%2B-+sqrt%28+448+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=304 ALIGN=MIDDLE  ALT=\"304\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=448 ALIGN=MIDDLE  ALT=\"448\"   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+=+%2812+%2B-+sqrt%28+448+%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"y+=+%2812+%2B-+sqrt%28+448+%29%29%2F%288%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=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   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+=+%2812+%2B-+8%2Asqrt%287%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"y+=+%2812+%2B-+8%2Asqrt%287%29%29%2F%288%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=y+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"y+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2812-8%2Asqrt%287%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"y+=+%2812-8%2Asqrt%287%29%29%2F%288%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 y are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"y+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2812-8%2Asqrt%287%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"y+=+%2812-8%2Asqrt%287%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "But remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x%5E2+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+%2812-8%2Asqrt%287%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x%5E2+=+%2812-8%2Asqrt%287%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Do you think you can take it from here?\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim<BR>\n" );
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