document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=415558>Question 415558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you show me the steps of solving the quadratic equation but in the other form that's -(b)+-square root of b squared minus 4ac over 2a because i know how to solve it but i don't understand it.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #291309 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=291309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation has to be in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 2 roots. You can have:<BR>\n" );
document.write( "(1) 2 real roots<BR>\n" );
document.write( "(2) 1 real root<BR>\n" );
document.write( "(3) 2 imaginary roots<BR>\n" );
document.write( "(4) no roots<BR>\n" );
document.write( "All this information can be gotten out of the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "notice the +- before the square root sign<BR>\n" );
document.write( "You could express the formula as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-b+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-b+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "These are the x-coordinates of the 2 roots of the equation<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+5x+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+5x+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The factors will look like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+-+x%5B1%5D%29%2A%28x+-+x%5B2%5D%29+ ALIGN=MIDDLE  ALT=\"+%28x+-+x%5B1%5D%29%2A%28x+-+x%5B2%5D%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2 ALIGN=MIDDLE  ALT=\"a+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+5 ALIGN=MIDDLE  ALT=\"b+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+3 ALIGN=MIDDLE  ALT=\"c+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-5+%2B+sqrt%28+5%5E2-4%2A2%2A3+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-5+%2B+sqrt%28+5%5E2-4%2A2%2A3+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-5+%2B+sqrt%28+25+-+24+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-5+%2B+sqrt%28+25+-+24+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-5+%2B+1+%29%2F4+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-5+%2B+1+%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the other root is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-5+-+sqrt%28+25+-+4%2A2%2A3+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-5+-+sqrt%28+25+-+4%2A2%2A3+%29%29%2F%282%2A2%29+\"   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+=+%28-5+-+sqrt%28+25+-+24+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-5+-+sqrt%28+25+-+24+%29%29%2F4+\"   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+=+%28-5+-+1%29%2F4+ ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-5+-+1%29%2F4+\"   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+=+-3%2F2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I can rewrite what I found as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+x%5B1%5D+=+0 ALIGN=MIDDLE  ALT=\"x+-+x%5B1%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+x%5B2%5D+=+0 ALIGN=MIDDLE  ALT=\"x+-+x%5B2%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+%283%2F2%29+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+%283%2F2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the factors of the equation are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+1%29%2A%28x+%2B+3%2F2%29+=+0 ALIGN=MIDDLE  ALT=\"+%28x+%2B+1%29%2A%28x+%2B+3%2F2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x+%2B+%283%2F2%29%2Ax+%2B+3%2F2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x+%2B+%283%2F2%29%2Ax+%2B+3%2F2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%285%2F2%29%2Ax+%2B+3%2F2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%285%2F2%29%2Ax+%2B+3%2F2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+5x+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+5x+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "which is the equation, so the roots are -1 and -3/2<BR>\n" );
document.write( "Here is the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-4%2C+4%2C+-2%2C+8%2C+2x%5E2+%2B+5x+%2B+3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-4%2C+4%2C+-2%2C+8%2C+2x%5E2+%2B+5x+%2B+3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );