document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88959>Question 88959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with the following problem?  I am supposed to solve this equation using the quadratic formula.  (1/y)-(1/y+5)=(1/4)\r<BR>\n" );
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document.write( "Thank you very much for any help you can provide. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64659 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=64659\">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=1%2Fy-1%2F%28y%2B5%29=1%2F4 ALIGN=MIDDLE  ALT=\"1%2Fy-1%2F%28y%2B5%29=1%2F4\"   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%28y%2B5%29%281%2Fy-1%2F%28y%2B5%29%29=4y%28y%2B5%29%281%2F4%29 ALIGN=MIDDLE  ALT=\"4y%28y%2B5%29%281%2Fy-1%2F%28y%2B5%29%29=4y%28y%2B5%29%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 4y(y+5)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y%2B5%29-4y=y%28y%2B5%29 ALIGN=MIDDLE  ALT=\"4%28y%2B5%29-4y=y%28y%2B5%29\"   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=4y%2B20-4y=y%5E2%2B5y ALIGN=MIDDLE  ALT=\"4y%2B20-4y=y%5E2%2B5y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute again\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20=y%5E2%2B5y ALIGN=MIDDLE  ALT=\"20=y%5E2%2B5y\"   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=0=y%5E2%2B5y-20 ALIGN=MIDDLE  ALT=\"0=y%5E2%2B5y-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 20 from both sides\r<BR>\n" );
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document.write( "Now 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=y%5E2%2B5%2Ay-20=0 ALIGN=MIDDLE  ALT=\"y%5E2%2B5%2Ay-20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5 ALIGN=MIDDLE  ALT=\"b=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-20 ALIGN=MIDDLE  ALT=\"c=-20\"   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+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A-20+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"y+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A-20+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=5, and c=-20\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A-20+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"y+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A-20+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 5 to get 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5+%2B-+sqrt%28+25%2B80+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"y+=+%28-5+%2B-+sqrt%28+25%2B80+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-20%2A1 ALIGN=MIDDLE  ALT=\"-4%2A-20%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80 ALIGN=MIDDLE  ALT=\"80\"   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+=+%28-5+%2B-+sqrt%28+105+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"y+=+%28-5+%2B-+sqrt%28+105+%29%29%2F%282%2A1%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+=+%28-5+%2B-+sqrt%28105%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"y+=+%28-5+%2B-+sqrt%28105%29%29%2F%282%2A1%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=y+=+%28-5+%2B-+sqrt%28105%29%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28-5+%2B-+sqrt%28105%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\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+=+%28-5+%2B+sqrt%28105%29%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28-5+%2B+sqrt%28105%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5+-+sqrt%28105%29%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28-5+-+sqrt%28105%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which split up to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%2F2%2Bsqrt%28105%29%2F2 ALIGN=MIDDLE  ALT=\"y=-5%2F2%2Bsqrt%28105%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%2F2-sqrt%28105%29%2F2 ALIGN=MIDDLE  ALT=\"y=-5%2F2-sqrt%28105%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.6234753829798 ALIGN=MIDDLE  ALT=\"y=2.6234753829798\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7.6234753829798 ALIGN=MIDDLE  ALT=\"y=-7.6234753829798\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.6234753829798 ALIGN=MIDDLE  ALT=\"y=2.6234753829798\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7.6234753829798 ALIGN=MIDDLE  ALT=\"y=-7.6234753829798\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5%2Ax-20 ALIGN=MIDDLE  ALT=\"x%5E2%2B5%2Ax-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace y with x), we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-17.6234753829798%2C+12.6234753829798%2C+-17.6234753829798%2C+12.6234753829798%2C1%2Ax%5E2%2B5%2Ax%2B-20%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when we use the root finder feature on a calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.6234753829798 ALIGN=MIDDLE  ALT=\"x=2.6234753829798\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7.6234753829798 ALIGN=MIDDLE  ALT=\"x=-7.6234753829798\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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