document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=754329>Question 754329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 25+15y+2y^2=228 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458981 by </B><A HREF=/tutors/aboutme.mpl?userid=vidya+pattar><B>vidya pattar(14)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vidya+pattar><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=458981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solution:\r<BR>\n" );
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document.write( "Here you have :<BR>\n" );
document.write( "25 + 15y + 2y^2 = 228<BR>\n" );
document.write( "now try to get rid of 228 from the right side.<BR>\n" );
document.write( "25 - 228 +15y + 2y^2 =0<BR>\n" );
document.write( "now combine the like terms :<BR>\n" );
document.write( "-223 + 15y + 2y^2 = 0<BR>\n" );
document.write( "now arange them in increasing order.<BR>\n" );
document.write( "2y^2 +15y - 223 = 0 <BR>\n" );
document.write( "now to solve for x you have use the quadratic rquation: <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B15x%2B-223+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B15x%2B-223+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2815%29%5E2-4%2A2%2A-223=2009 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2815%29%5E2-4%2A2%2A-223=2009\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2009 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-15%2B-sqrt%28+2009+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-15%2B-sqrt%28+2009+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+2009+%29%29%2F2%5C2+=+7.45546741550748 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+2009+%29%29%2F2%5C2+=+7.45546741550748\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2815%29-sqrt%28+2009+%29%29%2F2%5C2+=+-14.9554674155075 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2815%29-sqrt%28+2009+%29%29%2F2%5C2+=+-14.9554674155075\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B15x%2B-223 ALIGN=MIDDLE  ALT=\"2x%5E2%2B15x%2B-223\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B15x%2B-223+=+2%28x-7.45546741550748%29%2A%28x--14.9554674155075%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B15x%2B-223+=+2%28x-7.45546741550748%29%2A%28x--14.9554674155075%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 7.45546741550748, -14.9554674155075.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B15%2Ax%2B-223+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B15%2Ax%2B-223+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "so here you get \" \r<BR>\n" );
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document.write( "x =  (-15 +/- sqrt ( 15^2 - 4(2)(-223)) )/ 2(2)<BR>\n" );
document.write( "x = -15 +/- sqrt ( 2009)/4\r<BR>\n" );
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document.write( "hence we get after calculation x = 7.45  and  x = - 14.955 \r<BR>\n" );
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document.write( "Thanks & regards\r<BR>\n" );
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document.write( "Vidya pattar </SPAN>\n" );
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