document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=787552>Question 787552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Quadratic Formula to solve the equation in the interval [0, 2&#960;). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list. Round each answer to four decimal places.)\r<BR>\n" );
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document.write( "20 sin2 x &#8722; 21 sin x + 4 = 0\r<BR>\n" );
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document.write( "I get these answers -> x =0.2527,0.9273\r<BR>\n" );
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document.write( "But the EX has 4 solutions and I don't know how to get the last 2???????\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 #478238 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=478238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 20 sin^2(x) - 21 sin(x) + 4 = 0<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=20x%5E2%2B-21x%2B4+=+0 ALIGN=MIDDLE  ALT=\"20x%5E2%2B-21x%2B4+=+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" );
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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=%28-21%29%5E2-4%2A20%2A4=121 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-21%29%5E2-4%2A20%2A4=121\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=121 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--21%2B-sqrt%28+121+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--21%2B-sqrt%28+121+%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-%28-21%29%2Bsqrt%28+121+%29%29%2F2%5C20+=+0.8 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+121+%29%29%2F2%5C20+=+0.8\"   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-%28-21%29-sqrt%28+121+%29%29%2F2%5C20+=+0.25 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-21%29-sqrt%28+121+%29%29%2F2%5C20+=+0.25\"   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=20x%5E2%2B-21x%2B4 ALIGN=MIDDLE  ALT=\"20x%5E2%2B-21x%2B4\"   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=20x%5E2%2B-21x%2B4+=+%28x-0.8%29%2A%28x-0.25%29 ALIGN=MIDDLE  ALT=\"20x%5E2%2B-21x%2B4+=+%28x-0.8%29%2A%28x-0.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.8, 0.25.\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+20%2Ax%5E2%2B-21%2Ax%2B4+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+20%2Ax%5E2%2B-21%2Ax%2B4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "sin(x) = 0.8<BR>\n" );
document.write( "x = 0.9273<BR>\n" );
document.write( "x = pi - 0.9273 = 2.2134<BR>\n" );
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document.write( "sin(x) = 0.25<BR>\n" );
document.write( "x = 0.2527<BR>\n" );
document.write( "x = pi - 0.2527 = 2.8889 </SPAN>\n" );
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