document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=536440>Question 536440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2(8x+1)^2=90\r<BR>\n" );
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document.write( "Solve using quadratic formula<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352352 by </B><A HREF=/tutors/aboutme.mpl?userid=Maths68><B>Maths68(1474)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Maths68><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/cgi-bin/show-face.mpl?user=Maths68><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=352352\">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=2%288x%2B1%29%5E2=90 ALIGN=MIDDLE  ALT=\"2%288x%2B1%29%5E2=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide by 2 both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%288x%2B1%29%5E2%2F2=90%2F2 ALIGN=MIDDLE  ALT=\"2%288x%2B1%29%5E2%2F2=90%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%282%29%288x%2B1%29%5E2%2F2=cross%2890%29%2Fcross%282%29 ALIGN=MIDDLE  ALT=\"cross%282%29%288x%2B1%29%5E2%2F2=cross%2890%29%2Fcross%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288x%2B1%29%5E2=45 ALIGN=MIDDLE  ALT=\"%288x%2B1%29%5E2=45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x%5E2%2B16x%2B1=45 ALIGN=MIDDLE  ALT=\"64x%5E2%2B16x%2B1=45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x%5E2%2B16x%2B1-45=0 ALIGN=MIDDLE  ALT=\"64x%5E2%2B16x%2B1-45=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x%5E2%2B16x-44=0 ALIGN=MIDDLE  ALT=\"64x%5E2%2B16x-44=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\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=64x%5E2%2B16x%2B-44+=+0 ALIGN=MIDDLE  ALT=\"64x%5E2%2B16x%2B-44+=+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=%2816%29%5E2-4%2A64%2A-44=11520 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2816%29%5E2-4%2A64%2A-44=11520\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=11520 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+=+%28-16%2B-sqrt%28+11520+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-16%2B-sqrt%28+11520+%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-%2816%29%2Bsqrt%28+11520+%29%29%2F2%5C64+=+0.713525491562421 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+11520+%29%29%2F2%5C64+=+0.713525491562421\"   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-%2816%29-sqrt%28+11520+%29%29%2F2%5C64+=+-0.963525491562421 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2816%29-sqrt%28+11520+%29%29%2F2%5C64+=+-0.963525491562421\"   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=64x%5E2%2B16x%2B-44 ALIGN=MIDDLE  ALT=\"64x%5E2%2B16x%2B-44\"   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=64x%5E2%2B16x%2B-44+=+64%28x-0.713525491562421%29%2A%28x--0.963525491562421%29 ALIGN=MIDDLE  ALT=\"64x%5E2%2B16x%2B-44+=+64%28x-0.713525491562421%29%2A%28x--0.963525491562421%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.713525491562421, -0.963525491562421.\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+64%2Ax%5E2%2B16%2Ax%2B-44+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+64%2Ax%5E2%2B16%2Ax%2B-44+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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