document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76887>Question 76887</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131449729/algebrahomeworkh>Prealgebra and Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a triangle is 85 inches.  The sides are: 2x, 2x+5, and X squared + 3  Find the legths of the sides.\r<BR>\n" );
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document.write( "I though of putting them all together and then factoring, but it wasn't working out.  If someone could help me I would really appreciate it.\r<BR>\n" );
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document.write( "Thank you very much for your time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55118 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=55118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we add all of the sides we get the perimeter, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%2B%282x%2B5%29%2B%28x%5E2%2B3%29=85 ALIGN=MIDDLE  ALT=\"%282x%29%2B%282x%2B5%29%2B%28x%5E2%2B3%29=85\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B8-85=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B8-85=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms and get all terms to one side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-77=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-77=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can factor the left side\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=factoring_quadratics.solver>Factoring Quadratics with a leading coefficient of 1 (a=1)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>In order to factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%5E2%2B4%2Ax%2B-77 ALIGN=MIDDLE  ALT=\"1%2Ax%5E2%2B4%2Ax%2B-77\"   DISABLED_style= \"max-width:90%; height:auto;\" >, first we need to ask ourselves: What two numbers multiply to -77 and add to 4? Lets find out by listing all of the possible factors of -77<BR>\n" );
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document.write( "  Factors:<BR>\n" );
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document.write( "  1,7,11,77,<BR>\n" );
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document.write( "  -1,-7,-11,-77,List the negative factors as well. This will allow us to find all possible combinations<BR>\n" );
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document.write( "  These factors pair up to multiply to -77.<BR>\n" );
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document.write( "  (-1)*(77)=-77<BR>\n" );
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document.write( "  (-7)*(11)=-77<BR>\n" );
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document.write( "   Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4<BR>\n" );
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document.write( "  <TABLE><TR><TD>First Number</TD><TD >|</TD><TD >Second Number</TD><TD >|</TD><TD >Sum</TD></TR><TR><TD >1</TD><TD >|</TD><TD >-77</TD>|</TD><TD >|</TD><TD >1+(-77)=-76</TD></TR><TR><TD >7</TD><TD >|</TD><TD >-11</TD>|</TD><TD >|</TD><TD >7+(-11)=-4</TD></TR><TR><TD >-1</TD><TD >|</TD><TD >77</TD>|</TD><TD >|</TD><TD >(-1)+77=76</TD></TR><TR><TD >-7</TD><TD >|</TD><TD >11</TD>|</TD><TD >|</TD><TD >(-7)+11=4</TD></TR><TABLE>We can see from the table that -7 and 11 add to 4.So the two numbers that multiply to -77 and add to 4 are: -7 and 11\r\n" );
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document.write( "  Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:\r\n" );
document.write( "  \r\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ba%29%28x%2Bb%29 ALIGN=MIDDLE  ALT=\"%28x%2Ba%29%28x%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >substitute a=-7 and b=11\r\n" );
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document.write( "  So the equation becomes:\r\n" );
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document.write( "  (x-7)(x+11)\r\n" );
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document.write( "  Notice that if we foil (x-7)(x+11) we get the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%5E2%2B4%2Ax%2B-77 ALIGN=MIDDLE  ALT=\"1%2Ax%5E2%2B4%2Ax%2B-77\"   DISABLED_style= \"max-width:90%; height:auto;\" > again</TD></TR>\n" );
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document.write( "So the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-77=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-77=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%28x%2B11%29=0 ALIGN=MIDDLE  ALT=\"%28x-7%29%28x%2B11%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now set each term equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-7=0 ALIGN=MIDDLE  ALT=\"x-7=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=7 ALIGN=MIDDLE  ALT=\"x=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%2B11=0 ALIGN=MIDDLE  ALT=\"x%2B11=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=-11 ALIGN=MIDDLE  ALT=\"x=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > This answer doesn't make any sense (a negative length doesn't work)\r<BR>\n" );
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document.write( "So our answer is 7<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%287%29%29%2B%282%287%29%2B5%29%2B%28%287%29%5E2%2B3%29=85 ALIGN=MIDDLE  ALT=\"%282%287%29%29%2B%282%287%29%2B5%29%2B%28%287%29%5E2%2B3%29=85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814%29%2B%2814%2B5%29%2B%2849%2B3%29=85 ALIGN=MIDDLE  ALT=\"%2814%29%2B%2814%2B5%29%2B%2849%2B3%29=85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814%29%2B%2819%29%2B%2852%29=85 ALIGN=MIDDLE  ALT=\"%2814%29%2B%2819%29%2B%2852%29=85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85=85 ALIGN=MIDDLE  ALT=\"85=85\"   DISABLED_style= \"max-width:90%; height:auto;\" > works </SPAN>\n" );
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