document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115286>Question 115286</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find two consecutive odd integers whose product is 15 more than three times their sum.\r<BR>\n" );
document.write( "\n" );
document.write( "My guess is x(x+2)=3x+15, when I work this problem I have to use the quadratic formula to get an answer I don't think is correct, 1/2 +- square root of 15.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you<BR>\n" );
document.write( "LeeAnn </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83895 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=83895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let first number be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x ALIGN=MIDDLE  ALT=\"+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and next number to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B2 ALIGN=MIDDLE  ALT=\"+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "their product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "their sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B%28x%2B2%29 ALIGN=MIDDLE  ALT=\"+x%2B%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "given: product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=three ALIGN=MIDDLE  ALT=\"three\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+times ALIGN=MIDDLE  ALT=\"+times\"   DISABLED_style= \"max-width:90%; height:auto;\" > their sum, so we have: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B+%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"3%28x%2B+%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B2%29=3%28x%2B+%28x%2B2%29%29+%2B15 ALIGN=MIDDLE  ALT=\"x%28x%2B2%29=3%28x%2B+%28x%2B2%29%29+%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B2x+=+3%282x%2B2%29+%2B+15 ALIGN=MIDDLE  ALT=\"x%5E2+%2B2x+=+3%282x%2B2%29+%2B+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B2x+=+6x+%2B+6+%2B+15 ALIGN=MIDDLE  ALT=\"x%5E2+%2B2x+=+6x+%2B+6+%2B+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x+=+6x%2B+21 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x+=+6x%2B+21\"   DISABLED_style= \"max-width:90%; height:auto;\" >…………write quadratic equation in standard form\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B2x+-+6x-+21=0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B2x+-+6x-+21=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2++-+4x-+21=0 ALIGN=MIDDLE  ALT=\"x%5E2++-+4x-+21=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >…….use quadratic formula to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%2C2%5D=%28-%28-4%29+%2B-+sqrt+%28%28-4%29%5E2+-+4%2A1%2A%28-21%29+%29%29+%2F+%282%2A1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%2C2%5D=%284+%2B-+sqrt+%2816+%2B+84%29%29+%2F+2 ALIGN=MIDDLE  ALT=\"x%5B1%2C2%5D=%284+%2B-+sqrt+%2816+%2B+84%29%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%2C2%5D=%284+%2B-+sqrt+%28100%29%29+%2F+2 ALIGN=MIDDLE  ALT=\"x%5B1%2C2%5D=%284+%2B-+sqrt+%28100%29%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%2C2%5D=%284+%2B-+10%29+%2F+2 ALIGN=MIDDLE  ALT=\"x%5B1%2C2%5D=%284+%2B-+10%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..\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=x%5B1%2C2%5D=%284+%2B-+10%29+%2F+2 ALIGN=MIDDLE  ALT=\"x%5B1%2C2%5D=%284+%2B-+10%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=%284+%2B+10%29+%2F+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D=%284+%2B+10%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+14+%2F+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+14+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+7 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..first odd integer…solution (1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=%284+-+10%29+%2F+2 ALIGN=MIDDLE  ALT=\"x%5B2%5D=%284+-+10%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=+-+6+%2F+2 ALIGN=MIDDLE  ALT=\"x%5B2%5D=+-+6+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=+-+3 ALIGN=MIDDLE  ALT=\"x%5B2%5D=+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >……………….. first odd integer…solution (2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Second odd integer is: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+%2B2+=+7+%2B+2+=+9 ALIGN=MIDDLE  ALT=\"x%5B1%5D+%2B2+=+7+%2B+2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >……………………….. solution (1)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+%2B2+=+-3+%2B+2+=+-1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+%2B2+=+-3+%2B+2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >…………………… solution (2)\r<BR>\n" );
document.write( "\n" );
document.write( "Check both solutions:\r<BR>\n" );
document.write( "\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+7 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+7\"   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+%2B2+=+9 ALIGN=MIDDLE  ALT=\"x%5B1%5D+%2B2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >……………………….. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then their product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B2%29=+7%289%29+=+63 ALIGN=MIDDLE  ALT=\"x%28x%2B2%29=+7%289%29+=+63\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And their sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B%28x%2B2%29=+7+%2B+9+=+16+ ALIGN=MIDDLE  ALT=\"+x%2B%28x%2B2%29=+7+%2B+9+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>...than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=three ALIGN=MIDDLE  ALT=\"three\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+times ALIGN=MIDDLE  ALT=\"+times\"   DISABLED_style= \"max-width:90%; height:auto;\" > their sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A16=+48 ALIGN=MIDDLE  ALT=\"3%2A16=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Difference between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=63 ALIGN=MIDDLE  ALT=\"63\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=63+-+48+=+15 ALIGN=MIDDLE  ALT=\"63+-+48+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+-3 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+-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+%2B2+=+-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+%2B2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >……………………….. \r<BR>\n" );
document.write( "\n" );
document.write( "Then their product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B2%29=+-3%28-1%29+=+3 ALIGN=MIDDLE  ALT=\"x%28x%2B2%29=+-3%28-1%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "And their sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B%28x%2B2%29=+-3+%2B+-1+=+-4+ ALIGN=MIDDLE  ALT=\"+x%2B%28x%2B2%29=+-3+%2B+-1+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>...\r<BR>\n" );
document.write( "\n" );
document.write( "than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=three ALIGN=MIDDLE  ALT=\"three\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+times ALIGN=MIDDLE  ALT=\"+times\"   DISABLED_style= \"max-width:90%; height:auto;\" > their sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A-4=+-12 ALIGN=MIDDLE  ALT=\"3%2A-4=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Difference between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > is: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+-+%28-12%29+=+3+%2B+12+=+15 ALIGN=MIDDLE  ALT=\"3+-+%28-12%29+=+3+%2B+12+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >………..\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );