document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=410986>Question 410986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the quadratic formula to solve the following equation for x, show as much work as possible: 0 = 2x2 - 5x - 18.<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 #288897 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=288897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please use the \"^\" symbol (SHIFT+6) to indicate exponents. \"2x2\" could be interpreted as 2 times x times 2.<br><BR>\n" );
document.write( "The general quadratic equation is:<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( "You must learn this because 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( "is written in terms of the a, b and c from the genreal equation.<br><BR>\n" );
document.write( "With your equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2x%5E2+-+5x+-+18 ALIGN=MIDDLE  ALT=\"0+=+2x%5E2+-+5x+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = -5<BR>\n" );
document.write( "c = -18<BR>\n" );
document.write( "(If you don't see why b and c are negative, then look at the general equation. It is written with additions. So you have to write (ar least think of) your equation with additions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2x%5E2+%2B+%28-5x%29+%2B+%28-18%29 ALIGN=MIDDLE  ALT=\"0+=+2x%5E2+%2B+%28-5x%29+%2B+%28-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we just substitute these values into the formula and simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28-5%29+%2B-+sqrt%28%28-5%29%5E2+-+4%282%29%28-18%29%29%29%2F2%282%29 ALIGN=MIDDLE  ALT=\"x+=+-%28-5%29+%2B-+sqrt%28%28-5%29%5E2+-+4%282%29%28-18%29%29%29%2F2%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-5%29+%2B-+sqrt%2825+-+4%282%29%28-18%29%29%29%2F2%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29+%2B-+sqrt%2825+-+4%282%29%28-18%29%29%29%2F2%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=x+=+%28-%28-5%29+%2B-+sqrt%2825+%2B+144%29%29%2F2%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29+%2B-+sqrt%2825+%2B+144%29%29%2F2%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=x+=+%28-%28-5%29+%2B-+sqrt%28169%29%29%2F2%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29+%2B-+sqrt%28169%29%29%2F2%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=x+=+%285+%2B-+sqrt%28169%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28169%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+=+%285+%2B-+13%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+13%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Quadratic equations have two solutions. The \"plus or minus\" symbol in the formula is a shorthand way of expressing both solutions within the same expression. It is now time to write the two solutions separately. This last expression is a shorthand way of saying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B+13%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B+13%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+-+13%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%285+-+13%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can now continue with the simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+18%2F4 ALIGN=MIDDLE  ALT=\"x+=+18%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-8%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-8%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+=+9%2F2 ALIGN=MIDDLE  ALT=\"x+=+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2 ALIGN=MIDDLE  ALT=\"x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );