document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167137>Question 167137</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry Structure and Method book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have been trying to figure out this math problem and I can't get the answer. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!\r<BR>\n" );
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document.write( "Problem Solving Using Polynomial Equations<BR>\n" );
document.write( "Solve each problem. If there are two correct answers, give both of them.<BR>\n" );
document.write( "A rectangle is 15cm wide and 18cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116cm^2 less than the area of the original. Find the dimensions of the new rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123124 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangle is 15cm wide and 18cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116cm^2 less than the area of the original. Find the dimensions of the new rectangle.<BR>\n" );
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document.write( "Let x = amount decreased<BR>\n" );
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document.write( "new width = 15-x<BR>\n" );
document.write( "new length = 18-x<BR>\n" );
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document.write( "(15-x)(18-x) = 116<BR>\n" );
document.write( "270-15x-18x+x^2 = 116<BR>\n" );
document.write( "270-33x+x^2 = 116<BR>\n" );
document.write( "154-33x+x^2 = 0<BR>\n" );
document.write( "x^2-33x+154 = 0<BR>\n" );
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document.write( "Using the quadratic equation to solve we get:<BR>\n" );
document.write( "x = {27.374, 5.626}<BR>\n" );
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document.write( "We can toss out the 27.374 leaving us with <BR>\n" );
document.write( "x = 5.626 <BR>\n" );
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document.write( "new width = 15-x = 15-5.626 = 9.374 inches<BR>\n" );
document.write( "new length = 18-x = 18-5.626 = 12.374 inches<BR>\n" );
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document.write( "Solution: new rectangle is 9.374 by 12.374 inches<BR>\n" );
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document.write( "Details of quadratic:<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-33x%2B154+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-33x%2B154+=+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" );
document.write( "  <BR>\n" );
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=%28-33%29%5E2-4%2A1%2A154=473 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-33%29%5E2-4%2A1%2A154=473\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=473 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--33%2B-sqrt%28+473+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--33%2B-sqrt%28+473+%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-%28-33%29%2Bsqrt%28+473+%29%29%2F2%5C1+=+27.3742815854658 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-33%29%2Bsqrt%28+473+%29%29%2F2%5C1+=+27.3742815854658\"   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-%28-33%29-sqrt%28+473+%29%29%2F2%5C1+=+5.62571841453423 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-33%29-sqrt%28+473+%29%29%2F2%5C1+=+5.62571841453423\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-33x%2B154 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-33x%2B154\"   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-33x%2B154+=+1%28x-27.3742815854658%29%2A%28x-5.62571841453423%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-33x%2B154+=+1%28x-27.3742815854658%29%2A%28x-5.62571841453423%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 27.3742815854658, 5.62571841453423.\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-33%2Ax%2B154+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-33%2Ax%2B154+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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