document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190247>Question 1190247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the square of a number is added to 3 times the number,the sum is 108.Find the number.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821853 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The words say<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2Bx%5E2=108 ALIGN=MIDDLE  ALT=\"3x%2Bx%5E2=108\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That's a quadratic equation; get everything on one side and factor:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x-108=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-108=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With a negative constant term, the factorization has to be of the form (x+a)(x-b); so we need two numbers whose product is 108 and whose difference is 3 -- 12 and 9.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B12%29%28x-9%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B12%29%28x-9%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=-12 ALIGN=MIDDLE  ALT=\"x=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Check to see if both solutions to the equation are solutions to the original problem:<BR>\n" );
document.write( "x=-12: 3x+x^2 = -36+144 = 108 check<BR>\n" );
document.write( "x=9: 3x+x^2 = 27+81 = 108 check<br><BR>\n" );
document.write( "ANSWERS: -12 or 9<br><BR>\n" );
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