document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100219>Question 1100219</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem 1: When twice the second number is subtracted from the first number, the result is -18. The square of the sum of the first number and 2 is equal to the second number minus 3.\r<BR>\n" );
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document.write( "Problem 2: Twice the square of the first number minus the second number is -3. The square of the sum of the first number and 5 is equal to the second number minus 2.\r<BR>\n" );
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document.write( "Please include \"let statements\" and equations. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714722 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem 1:<BR>\n" );
document.write( "let a = the first number<BR>\n" );
document.write( "let b = the second number<BR>\n" );
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document.write( "Write an equation for each statement<BR>\n" );
document.write( "\"When twice the second number is subtracted from the first number, the result is -18.\"<BR>\n" );
document.write( "a - 2b = -18<BR>\n" );
document.write( "rearrange for substitution in the 2nd equation<BR>\n" );
document.write( "-2b = -a - 18<BR>\n" );
document.write( "multiply by -1<BR>\n" );
document.write( "2b = a + 18<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B18%29%2F2 ALIGN=MIDDLE  ALT=\"%28a%2B18%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"The square of the sum of the first number and 2 is equal to the second number minus 3.\"<BR>\n" );
document.write( "(a+2)^2 = b - 3<BR>\n" );
document.write( "FOIL (a+2)(a+2)<BR>\n" );
document.write( "a^2 + 4a + 4 = b - 3<BR>\n" );
document.write( "replace b with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B18%29%2F2 ALIGN=MIDDLE  ALT=\"%28a%2B18%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a^2 + 4a + 4 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B18%29%2F2 ALIGN=MIDDLE  ALT=\"%28a%2B18%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 3<BR>\n" );
document.write( "get rid of the fraction, multiply by 2<BR>\n" );
document.write( "2a^2 + 8a + 8 = a + 18 - 6<BR>\n" );
document.write( "2a^2 + 8a + 8 = a + 12<BR>\n" );
document.write( "2a^2 + 8a - a + 8 - 12 = 0<BR>\n" );
document.write( "2a^2 + 7a - 4 = 0<BR>\n" );
document.write( "Assuming they are using integers, it must factor<BR>\n" );
document.write( "(2a-1)(a+4) = 0<BR>\n" );
document.write( "two solutions<BR>\n" );
document.write( "a = 1/2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "a = -4 the integer solution is what we want here<BR>\n" );
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document.write( "find b using the 1st equation when a = -4<BR>\n" );
document.write( "-4 - 2b = -18<BR>\n" );
document.write( "multiply by -1<BR>\n" );
document.write( "4 + 2b = 18<BR>\n" );
document.write( "2b = 18 - 4<BR>\n" );
document.write( "2b = 14<BR>\n" );
document.write( "b = 7<BR>\n" );
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document.write( "1st number is -4, 2nd number is +7<BR>\n" );
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document.write( "see if that checks out in the 2nd equation<BR>\n" );
document.write( "(-4+2)^2 = 7 - 3<BR>\n" );
document.write( "-2^2 = 4<BR>\n" );
document.write( "4 = 4<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Problem 2: Much like the first problem<BR>\n" );
document.write( "Twice the square of the first number minus the second number is -3.<BR>\n" );
document.write( "2a^2 - b = -3<BR>\n" );
document.write( "-b = -2a^2 - 3<BR>\n" );
document.write( "b = 2a^2 + 3<BR>\n" );
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document.write( " The square of the sum of the first number and 5 is equal to the second number minus 2.<BR>\n" );
document.write( "(a+5)^2 = b - 2 <BR>\n" );
document.write( "FOIL, Replace b with 2a^2 + 3<BR>\n" );
document.write( "a^2 + 10a + 25 = 2a^2 + 3 - 2<BR>\n" );
document.write( "a^2 + 10a + 25 = 2a^2 + 1<BR>\n" );
document.write( "combine on the right<BR>\n" );
document.write( "0 = 2a^2 - a^2 - 10a - 25 + 1<BR>\n" );
document.write( "0 = a^2 - 10a - 24<BR>\n" );
document.write( "(a - 12)(a + 2) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "a = 12<BR>\n" );
document.write( "and <BR>\n" );
document.write( "a = -2<BR>\n" );
document.write( "Find b when a = 12<BR>\n" );
document.write( "b = 2(12^2) + 3<BR>\n" );
document.write( "b = 2(144) + 3<BR>\n" );
document.write( "b = 289<BR>\n" );
document.write( "See if that works in the 2nd equation<BR>\n" );
document.write( "(12 + 5)^2 = 289 - 2<BR>\n" );
document.write( "17^2 = 287<BR>\n" );
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document.write( "Why don't you find b when a = -2 and check that out\r<BR>\n" );
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document.write( " </SPAN>\n" );
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