document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65840>Question 65840</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/093979862x/algebrahomeworkh>An Incremental Development</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Use the discriminant to determine the kinds of numbers that will satisfy the equation 5x = x^2 - 3. Do not solve </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46591 by </B><A HREF=/tutors/aboutme.mpl?userid=303795><B>303795(602)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=303795><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=46591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rearrange the equation to get it in the <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;\" > form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=x%5E2-3 ALIGN=MIDDLE  ALT=\"5x=x%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 5x from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-5x=x%5E2-5x-3 ALIGN=MIDDLE  ALT=\"5x-5x=x%5E2-5x-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%5E2-5x-3=0 ALIGN=MIDDLE  ALT=\"x%5E2-5x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The discriminant is found using the formula <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4%2Aa%2Ac ALIGN=MIDDLE  ALT=\"b%5E2-4%2Aa%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this example a=1, b=-5 and c=-3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29%5E2-4%2A1%2A%28-3%29 ALIGN=MIDDLE  ALT=\"%28-5%29%5E2-4%2A1%2A%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25-%28-12%29 ALIGN=MIDDLE  ALT=\"25-%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=37<BR>\n" );
document.write( "The number is positive so there will be two real solutions to the equation.<BR>\n" );
document.write( "(a value of zero implies one solution and a negative value implies no real solution but two solutions involving complex numbers.) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );