document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=180563>Question 180563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A business invests $8,000 in a savings account for two years. At the beginning of the second year an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #135331 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=135331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assuming the interest rate is the same for both amounts invested<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8000%2B8000x%2B%288000%2B8000x%29x%2B2500%2B2500x=11445 ALIGN=MIDDLE  ALT=\"8000%2B8000x%2B%288000%2B8000x%29x%2B2500%2B2500x=11445\"   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=8000%2B8000x%2B8000x%2B8000x%5E2%2B2500%2B2500x=11445 ALIGN=MIDDLE  ALT=\"8000%2B8000x%2B8000x%2B8000x%5E2%2B2500%2B2500x=11445\"   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=8000x%5E2%2B18500x-945=0 ALIGN=MIDDLE  ALT=\"8000x%5E2%2B18500x-945=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x=.05 and -2.36<BR>\n" );
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document.write( "throw out the negative<BR>\n" );
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document.write( "interest rate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05%28100%29=highlight%285%29 ALIGN=MIDDLE  ALT=\".05%28100%29=highlight%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >%<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=8000x%5E2%2B18500x%2B-945+=+0 ALIGN=MIDDLE  ALT=\"8000x%5E2%2B18500x%2B-945+=+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=%2818500%29%5E2-4%2A8000%2A-945=372490000 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2818500%29%5E2-4%2A8000%2A-945=372490000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=372490000 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+=+%28-18500%2B-sqrt%28+372490000+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-18500%2B-sqrt%28+372490000+%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-%2818500%29%2Bsqrt%28+372490000+%29%29%2F2%5C8000+=+0.05 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2818500%29%2Bsqrt%28+372490000+%29%29%2F2%5C8000+=+0.05\"   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-%2818500%29-sqrt%28+372490000+%29%29%2F2%5C8000+=+-2.3625 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2818500%29-sqrt%28+372490000+%29%29%2F2%5C8000+=+-2.3625\"   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=8000x%5E2%2B18500x%2B-945 ALIGN=MIDDLE  ALT=\"8000x%5E2%2B18500x%2B-945\"   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=8000x%5E2%2B18500x%2B-945+=+%28x-0.05%29%2A%28x--2.3625%29 ALIGN=MIDDLE  ALT=\"8000x%5E2%2B18500x%2B-945+=+%28x-0.05%29%2A%28x--2.3625%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.05, -2.3625.\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+8000%2Ax%5E2%2B18500%2Ax%2B-945+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8000%2Ax%5E2%2B18500%2Ax%2B-945+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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