document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248346>Question 248346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here are three questions I need help with:\r<BR>\n" );
document.write( "\n" );
document.write( "1.) 5d^2 - 10d = 0       (factoring problem)\r<BR>\n" );
document.write( "\n" );
document.write( "2.) 8x^2 = 16            (factoring problem)\r<BR>\n" );
document.write( "\n" );
document.write( "3.) 3m^2 - 5m = -2       (factoring problem)\r<BR>\n" );
document.write( "\n" );
document.write( "And my teacher only likes the answers in fractions or radicals, no decimals.<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180986 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=180986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.) 5d^2 - 10d = 0       (factoring problem)<BR>\n" );
document.write( "5d(d-2)=0<BR>\n" );
document.write( "d=0 and d=2<BR>\n" );
document.write( "2.) 8x^2 = 16            (factoring problem)<BR>\n" );
document.write( "8(x^2)=8*2<BR>\n" );
document.write( "divide by 2<BR>\n" );
document.write( "x^2=2<BR>\n" );
document.write( "x=+\-sqrt2<BR>\n" );
document.write( "3.) 3m^2 - 5m = -2       (factoring problem)<BR>\n" );
document.write( "divide by 3<BR>\n" );
document.write( "m^2-5/3m=-2/3<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=1x%5E2%2B-1.66666666666667x%2B0.666666666666667+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1.66666666666667x%2B0.666666666666667+=+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=%28-1.66666666666667%29%5E2-4%2A1%2A0.666666666666667=0.111111111111121 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1.66666666666667%29%5E2-4%2A1%2A0.666666666666667=0.111111111111121\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=0.111111111111121 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--1.66666666666667%2B-sqrt%28+0.111111111111121+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1.66666666666667%2B-sqrt%28+0.111111111111121+%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-%28-1.66666666666667%29%2Bsqrt%28+0.111111111111121+%29%29%2F2%5C1+=+1.00000000000001 ALIGN=MIDDLE   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-%28-1.66666666666667%29-sqrt%28+0.111111111111121+%29%29%2F2%5C1+=+0.666666666666661 ALIGN=MIDDLE   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=1x%5E2%2B-1.66666666666667x%2B0.666666666666667 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1.66666666666667x%2B0.666666666666667\"   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=1x%5E2%2B-1.66666666666667x%2B0.666666666666667+=+1%28x-1.00000000000001%29%2A%28x-0.666666666666661%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.00000000000001, 0.666666666666661.\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+1%2Ax%5E2%2B-1.66666666666667%2Ax%2B0.666666666666667+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "complete the square<BR>\n" );
document.write( "add 25/36 to both sides\r<BR>\n" );
document.write( "\n" );
document.write( "m^2-5/3m+25/36=-24/36+25/36=1 /36<BR>\n" );
document.write( "factor<BR>\n" );
document.write( "(m-5/6)^2=(1/6)^2<BR>\n" );
document.write( "m-5/6=+\- 1/6<BR>\n" );
document.write( "add 5/6 to both sides<BR>\n" );
document.write( "m=4/6=2/3<BR>\n" );
document.write( "m=6/6=1<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );