document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251684>Question 251684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem: Originally, a rectangle was three times as long as it is wide. When 2 cm were subtracted from the length and 5 cm were added to the width, the resulting rectangle had an area of 90 cm squared. Find the dimensions of the new rectangle.\r<BR>\n" );
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document.write( "hmmmm, I tried this problem...but I keep getting decimal answers when solving :/ We are supposed to use only one variable in the actual equation, and use Quadratic equations to solve. \r<BR>\n" );
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document.write( "My Attempt:\r<BR>\n" );
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document.write( "w=width<BR>\n" );
document.write( "l=length<BR>\n" );
document.write( "l=3w\r<BR>\n" );
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document.write( "Formula-<BR>\n" );
document.write( "A=width(length)<BR>\n" );
document.write( "(3w-2)(w+5)=90<BR>\n" );
document.write( "Then I foiled and got:<BR>\n" );
document.write( "3w^2+13w-100=0<BR>\n" );
document.write( "And I get stuck there :/ I don't think it factors and I'm not sure if I foiled wrong or set it up wrong. :/ Help me, please? Thanks :)\r<BR>\n" );
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document.write( "I put this under Algebra, although I am in Algebra II, I hope that is fine :D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183361 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> so far so good<BR>\n" );
document.write( "It factors to<BR>\n" );
document.write( "(w-4)(3w+25) = 0<BR>\n" );
document.write( "which yields two answers 4 and -25/3<BR>\n" );
document.write( "We need a positive answer.<BR>\n" );
document.write( "notice that below that even factored out the 3<BR>\n" );
document.write( "and got 3*(w-4)*(w+8.33)<BR>\n" );
document.write( "so 3w^2+13w-100=3*(w^2+4 1/3 w-33 1/3)which factors into 3*(w-4)*(w+8 1/3)<BR>\n" );
document.write( "You could also have used the quadratic formula. See below<BR>\n" );
document.write( "which would have been the best choice after not finding factors.<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=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w%5E2%2B13w%2B-100+=+0 ALIGN=MIDDLE  ALT=\"3w%5E2%2B13w%2B-100+=+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=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%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=%2813%29%5E2-4%2A3%2A-100=1369 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2813%29%5E2-4%2A3%2A-100=1369\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1369 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+=+%28-13%2B-sqrt%28+1369+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-13%2B-sqrt%28+1369+%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=w%5B1%5D+=+%28-%2813%29%2Bsqrt%28+1369+%29%29%2F2%5C3+=+4 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%2813%29%2Bsqrt%28+1369+%29%29%2F2%5C3+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%2813%29-sqrt%28+1369+%29%29%2F2%5C3+=+-8.33333333333333 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%2813%29-sqrt%28+1369+%29%29%2F2%5C3+=+-8.33333333333333\"   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=3w%5E2%2B13w%2B-100 ALIGN=MIDDLE  ALT=\"3w%5E2%2B13w%2B-100\"   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=3w%5E2%2B13w%2B-100+=+3%28w-4%29%2A%28w--8.33333333333333%29 ALIGN=MIDDLE  ALT=\"3w%5E2%2B13w%2B-100+=+3%28w-4%29%2A%28w--8.33333333333333%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4, -8.33333333333333.\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+3%2Ax%5E2%2B13%2Ax%2B-100+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B13%2Ax%2B-100+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\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=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B4.33333333333333w%2B-33.3333333333333+=+0 ALIGN=MIDDLE  ALT=\"1w%5E2%2B4.33333333333333w%2B-33.3333333333333+=+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=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%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=%284.33333333333333%29%5E2-4%2A1%2A-33.3333333333333=152.111111111111 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284.33333333333333%29%5E2-4%2A1%2A-33.3333333333333=152.111111111111\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=152.111111111111 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+=+%28-4.33333333333333%2B-sqrt%28+152.111111111111+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4.33333333333333%2B-sqrt%28+152.111111111111+%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=w%5B1%5D+=+%28-%284.33333333333333%29%2Bsqrt%28+152.111111111111+%29%29%2F2%5C1+=+4 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%284.33333333333333%29%2Bsqrt%28+152.111111111111+%29%29%2F2%5C1+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%284.33333333333333%29-sqrt%28+152.111111111111+%29%29%2F2%5C1+=+-8.33333333333333 ALIGN=MIDDLE   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=1w%5E2%2B4.33333333333333w%2B-33.3333333333333 ALIGN=MIDDLE  ALT=\"1w%5E2%2B4.33333333333333w%2B-33.3333333333333\"   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=1w%5E2%2B4.33333333333333w%2B-33.3333333333333+=+1%28w-4%29%2A%28w--8.33333333333333%29 ALIGN=MIDDLE  ALT=\"1w%5E2%2B4.33333333333333w%2B-33.3333333333333+=+1%28w-4%29%2A%28w--8.33333333333333%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4, -8.33333333333333.\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%2B4.33333333333333%2Ax%2B-33.3333333333333+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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