document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172689>Question 172689</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I really dont understand this problem can some pleas help me thank you\r<BR>\n" );
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document.write( "A business invests $10,000 in a savings account for two years.  At the beginning of the second year, an additional $3500 is invested.  At the end of the second year, the account balance is $15,569.75.  What was the annual interest rate? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127557 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=127557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2.10000(x+1)(x+1)+3500(x+1)=15569.75------>where x is the interest rate<BR>\n" );
document.write( ".... dealing with a quadratic formula.....<BR>\n" );
document.write( "when you solve this email me and I will let you know if you have the correct answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%28x%5E2%2B2x%2B1%29%2B3500x%2B3500=15569.75 ALIGN=MIDDLE  ALT=\"10000%28x%5E2%2B2x%2B1%29%2B3500x%2B3500=15569.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000x%5E2%2B20000x%2B10000%2B3500x%2B3500=15569.75 ALIGN=MIDDLE  ALT=\"10000x%5E2%2B20000x%2B10000%2B3500x%2B3500=15569.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000x%5E2%2B23500x-2069.75=0 ALIGN=MIDDLE  ALT=\"10000x%5E2%2B23500x-2069.75=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "drop the negative value<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=.085%2Cx=-2.64%29 ALIGN=MIDDLE  ALT=\"system%28x=.085%2Cx=-2.64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=.085%29 ALIGN=MIDDLE  ALT=\"highlight%28x=.085%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >or 8.5%\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=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=10000x%5E2%2B23500x%2B-2069+=+0 ALIGN=MIDDLE  ALT=\"10000x%5E2%2B23500x%2B-2069+=+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=%2823500%29%5E2-4%2A10000%2A-2069=635010000 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2823500%29%5E2-4%2A10000%2A-2069=635010000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=635010000 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+=+%28-23500%2B-sqrt%28+635010000+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-23500%2B-sqrt%28+635010000+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2823500%29%2Bsqrt%28+635010000+%29%29%2F2%5C10000+=+0.0849702377437334 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2823500%29%2Bsqrt%28+635010000+%29%29%2F2%5C10000+=+0.0849702377437334\"   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-%2823500%29-sqrt%28+635010000+%29%29%2F2%5C10000+=+-2.43497023774373 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2823500%29-sqrt%28+635010000+%29%29%2F2%5C10000+=+-2.43497023774373\"   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=10000x%5E2%2B23500x%2B-2069 ALIGN=MIDDLE  ALT=\"10000x%5E2%2B23500x%2B-2069\"   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=10000x%5E2%2B23500x%2B-2069+=+10000%28x-0.0849702377437334%29%2A%28x--2.43497023774373%29 ALIGN=MIDDLE  ALT=\"10000x%5E2%2B23500x%2B-2069+=+10000%28x-0.0849702377437334%29%2A%28x--2.43497023774373%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.0849702377437334, -2.43497023774373.\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+10000%2Ax%5E2%2B23500%2Ax%2B-2069+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10000%2Ax%5E2%2B23500%2Ax%2B-2069+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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