document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201620>Question 201620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve equation with quadratic formula<BR>\n" );
document.write( "3n^2-15=-4n </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151818 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=151818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To use the quadratic formula we must first get the equation into the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This means:<ol><li>Get one side equal to zero</li><Change any subtractions on the non-zero side to additions of the opposites</li><li>Use the Commutative property of addition to rearrange the non-zero side in order from highest exponent to lowest.</li></ol><BR>\n" );
document.write( "Using these steps on your equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+-+15+=+-4n ALIGN=MIDDLE  ALT=\"3n%5E2+-+15+=+-4n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1. Make one side zero. By adding 4n to both sides the right side will become zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+-+15+%2B+4n+=+0 ALIGN=MIDDLE  ALT=\"3n%5E2+-+15+%2B+4n+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. Change subtractions to additions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+%2B+%28-15%29+%2B+4n+=+0 ALIGN=MIDDLE  ALT=\"3n%5E2+%2B+%28-15%29+%2B+4n+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. Rearrange<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+%2B+4n+%2B+%28-15%29+=+0 ALIGN=MIDDLE  ALT=\"3n%5E2+%2B+4n+%2B+%28-15%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we have the equation in the proper form for the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looking at your rearranged equation we should be able to tell that<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "b = 4<BR>\n" );
document.write( "c = -15<BR>\n" );
document.write( "Substituting these into the appropriate places in the formula we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28+-%284%29+%2B-+sqrt%28%284%29%5E2+-+4%283%29%28-15%29%29%29%2F2%283%29 ALIGN=MIDDLE  ALT=\"x+=+%28+-%284%29+%2B-+sqrt%28%284%29%5E2+-+4%283%29%28-15%29%29%29%2F2%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Squaring the 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28+-4+%2B-+sqrt%2816+-+4%283%29%28-15%29%29%29%2F2%283%29 ALIGN=MIDDLE  ALT=\"x+=+%28+-4+%2B-+sqrt%2816+-+4%283%29%28-15%29%29%29%2F2%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28+-4+%2B-+sqrt%2816+-+%28-180%29%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28+-4+%2B-+sqrt%2816+-+%28-180%29%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying inside the square root<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28+-4+%2B-+sqrt%28196%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28+-4+%2B-+sqrt%28196%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28196%29+=+14 ALIGN=MIDDLE  ALT=\"sqrt%28196%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substituting we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+14%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+14%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Splitting the +- we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B+14%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B+14%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+-+14%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-4+-+14%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying each:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10%2F6+=+1%264%2F6+=+1%262%2F3 ALIGN=MIDDLE  ALT=\"x+=+10%2F6+=+1%264%2F6+=+1%262%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-18%2F6+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-18%2F6+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%262%2F3 ALIGN=MIDDLE  ALT=\"x+=+1%262%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );