document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999558>Question 999558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve the following:<BR>\n" );
document.write( "Three consecutive even integers are such that the third number squared increased by the product of the other two numbers is 184.  Find the numbers.\r<BR>\n" );
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document.write( "I tried this but it's not checking.<BR>\n" );
document.write( "Let x= first even integer<BR>\n" );
document.write( "    x+2= second even integer<BR>\n" );
document.write( "    x+4= third even integer<BR>\n" );
document.write( "(x+4)^2 +x(x+2)=184<BR>\n" );
document.write( "(x+4)^2 +x(x+2)-184=0<BR>\n" );
document.write( "x^2+8x+16+x^2+2x-184=0<BR>\n" );
document.write( "2x^2+10x-168=0<BR>\n" );
document.write( "x^2+5x-84=0\r<BR>\n" );
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document.write( "(x+12)(x-7)=0<BR>\n" );
document.write( "x+12=0 x=-12<BR>\n" );
document.write( "x-7=0 x=7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617164 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=617164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You should completely retry what you did, but start THIS WAY for your numbers:\r<BR>\n" );
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document.write( "x can be any integer.<BR>\n" );
document.write( "2x will then be the first of your consecutive EVEN integers. The next two are  2x+2  and  2x+4.\r<BR>\n" );
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document.write( "Now your consecutive EVEN integers are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x%2C+2x%2B2%2C2x%2B4%29 ALIGN=MIDDLE  ALT=\"system%282x%2C+2x%2B2%2C2x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve the problem now, according to those expressions.\r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "Upon rechecking your original work, the steps are still correct, regardless of the \"x\" or the \"2x\".  The step which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B12%29%28x-7%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B12%29%28x-7%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > WILL give what you need.  The assumption was that x could be one of the even numbers.\r<BR>\n" );
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document.write( "Zero-Product Rule says that either x+12=0, leading directly to x=-12, or that x-7=0, leading directly to x=7.  You KNOW that x=7 cannot be acceptable because this is ODD, and your description and question specified finding consecutive EVEN integers.  You must then accept the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-12%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > result.  \r<BR>\n" );
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document.write( "You know the rest.  Either way, test the results. </SPAN>\n" );
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