document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=722271>Question 722271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please show me all steps to the factoring and solving?  Also could you please show me how to check my solution back into the original equation?<BR>\n" );
document.write( "For the Quadratic Formula problem, could you please include readable notation while you are working the computational steps?<BR>\n" );
document.write( "Could you please show me the final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.<BR>\n" );
document.write( "If possible and applicable, could you please show me how to incorporate the following four math vocabulary words into my steps?<BR>\n" );
document.write( "-Quadratic formula <BR>\n" );
document.write( "-Factoring <BR>\n" );
document.write( "-Completing the square <BR>\n" );
document.write( "-Discriminant \r<BR>\n" );
document.write( "\n" );
document.write( "1.	2m^2 – m – 15 = 0<BR>\n" );
document.write( "2.	2y^2 - 3y – 6 = 0<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #442710 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=442710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "BEWARE: The Algebra.com system is cutting-off some of the expressions I am trying to write.  Not my fault.!\r<BR>\n" );
document.write( "\n" );
document.write( "A little bit of help on #1, but you must still study (your textbook) to make the best sense of it:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2+%96+m+%96+15+=+0 ALIGN=MIDDLE  ALT=\"2m%5E2+%96+m+%96+15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can try to factor by using the format, (2m_______)(m________), and look for pairs of numbers which give the product of -15.  Note, according to F.O.I.L. multiplication method, the O and I products must sum to -m.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What works?  15,1; 3,5; 5,3; 1,15?<BR>\n" );
document.write( "The 5,3 combination seems to do something useful.  <BR>\n" );
document.write( "(2m_____5)(m_______3).  Now you need to decide which operation in each binomial.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Skipping that and going to quadratic formula and discriminant:<BR>\n" );
document.write( "Know that <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;\" > is the discriminant for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Applying discriminant for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2-m-15 ALIGN=MIDDLE  ALT=\"2m%5E2-m-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E2-4%2A%282%29%2A%28-15%29=121 ALIGN=MIDDLE  ALT=\"%28-1%29%5E2-4%2A%282%29%2A%28-15%29=121\"   DISABLED_style= \"max-width:90%; height:auto;\" >, POSITIVE 121.  Read your book to know what this means.  How many Real solutions?  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Completing the Square allows you to change this general form equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2+%96+m+%96+15+=+0 ALIGN=MIDDLE  ALT=\"2m%5E2+%96+m+%96+15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, into standard form.  Standard form allows you to easily understand the graph of the equation.  The part of the equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2-m ALIGN=MIDDLE  ALT=\"2m%5E2-m\"   DISABLED_style= \"max-width:90%; height:auto;\" >, represents a rectangle.  The given equation does not really need completion of the square because it is found to be factorable to solve for m, but if you wished to have a graph or know more about the graph, then Completing the square may be very useful.  You would first factor the 2 from the rectangular expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2-m ALIGN=MIDDLE  ALT=\"2m%5E2-m\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then ADD and SUBTRACT the square term, which is like a missing square piece obtained from examening the actual rectangle represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2-%281%2F2%29m ALIGN=MIDDLE  ALT=\"m%5E2-%281%2F2%29m\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If you would draw the picture, you will find that the term to use is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%281%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  I omit the rest of the process here.  See and study your book.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2-m=2%28m%5E2-%281%2F2%29m%29 ALIGN=MIDDLE  ALT=\"2m%5E2-m=2%28m%5E2-%281%2F2%29m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28m%5E2-%281%2F2%29m+%2B+1%2F16%29+-+%281%2F16%29%2A2 ALIGN=MIDDLE  ALT=\"2%28m%5E2-%281%2F2%29m+%2B+1%2F16%29+-+%281%2F16%29%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,....<BR>\n" );
document.write( "... will get you started. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );