document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081746>Question 1081746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three consecutive positive integers such that the square of the first increased by the last is 22. \r<BR>\n" );
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document.write( "Please show the work.I know the answer(4,5,6) but the other tutor didn't show how he got this answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695768 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=695768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the first integer. The value of x is positive, so x > 0.\r<BR>\n" );
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document.write( "The next integer after x is x+1 which is the second number of the consecutive integer string. \r<BR>\n" );
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document.write( "The last integer of this grouping is (x+1)+1 = x+1+1 = x+2\r<BR>\n" );
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document.write( "The three integers, in terms of x, are<BR>\n" );
document.write( "x<BR>\n" );
document.write( "x+1<BR>\n" );
document.write( "x+2\r<BR>\n" );
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document.write( "Keep in mind that x is just a placeholder for some unknown number. \r<BR>\n" );
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document.write( "We're told that \"the square of the first increased by the last is 22\", meaning that...\r<BR>\n" );
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document.write( "(first integer of group)^2 + (last integer of group) = 22\r<BR>\n" );
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document.write( "Using the variable expressions set up above, we would end up with\r<BR>\n" );
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document.write( "(x)^2 + (x+2) = 22\r<BR>\n" );
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document.write( "Let's get everything to one side, simplify and then factor to solve for x\r<BR>\n" );
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document.write( "(x)^2 + (x+2) = 22<BR>\n" );
document.write( "x^2 + x+2 - 22 = 0<BR>\n" );
document.write( "x^2 + x - 20 = 0<BR>\n" );
document.write( "(x+5)(x-4) = 0 ... see note below<BR>\n" );
document.write( "x+5 = 0 or x-4 = 0<BR>\n" );
document.write( "x = -5 or x = 4\r<BR>\n" );
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document.write( "Note: to factor, you need to find two numbers that multiply to -20 and add to 1. Those two numbers are +5 and -4. \r<BR>\n" );
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document.write( "The two solutions are x = -5 or x = 4. However, recall that these integers are positive. Since x > 0, this rules out x = -5. The only practical solution is x = 4.\r<BR>\n" );
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document.write( "If x = 4, then<BR>\n" );
document.write( "first integer = x = 4<BR>\n" );
document.write( "second integer = x+1 = 4+1 = 5<BR>\n" );
document.write( "third integer = x+2 = 4+2 = 6\r<BR>\n" );
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document.write( "Which is why the ordered triple solution is (4,5,6) </SPAN>\n" );
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