document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168019>Question 168019</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1592009425/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> if the product of two consecutive integers is decreased by 20 times the greater integer, the result is 442.find the integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123833 by </B><A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><B>KnightOwlTutor(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><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=KnightOwlTutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> X=first #\r<BR>\n" );
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document.write( "x+1=2nd #\r<BR>\n" );
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document.write( "The equation is as follows\r<BR>\n" );
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document.write( "(x)(x+1)-20(x+1)=442\r<BR>\n" );
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document.write( "mulitply the terms to get:\r<BR>\n" );
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document.write( "x^2+x-20x-20=442\r<BR>\n" );
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document.write( "Combine like terms\r<BR>\n" );
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document.write( "x^2-19x-20=442\r<BR>\n" );
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document.write( "Add 20 to both sides\r<BR>\n" );
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document.write( "x^2-19x=462\r<BR>\n" );
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document.write( "Subtract 462 from both sides\r<BR>\n" );
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document.write( "x^2-19x-462=0\r<BR>\n" );
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document.write( "This is a quadratic eqation or parabola<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=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-19x%2B-462+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-19x%2B-462+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-19%29%5E2-4%2A1%2A-462=2209 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-19%29%5E2-4%2A1%2A-462=2209\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2209 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--19%2B-sqrt%28+2209+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--19%2B-sqrt%28+2209+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+2209+%29%29%2F2%5C1+=+33 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+2209+%29%29%2F2%5C1+=+33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-19%29-sqrt%28+2209+%29%29%2F2%5C1+=+-14 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-19%29-sqrt%28+2209+%29%29%2F2%5C1+=+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-19x%2B-462 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-19x%2B-462\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-19x%2B-462+=+1%28x-33%29%2A%28x--14%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-19x%2B-462+=+1%28x-33%29%2A%28x--14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 33, -14.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B-462+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B-462+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "The solutions to this equation is -14,33\r<BR>\n" );
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document.write( "Since the number in question is not negative the only solution is 33. Let's check our answer.\r<BR>\n" );
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document.write( "(33)(34)-20(34)=442\r<BR>\n" );
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document.write( "1,122-680=442\r<BR>\n" );
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document.write( " </SPAN>\n" );
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