document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001690>Question 1001690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2sin^2x=3sinx+5<BR>\n" );
document.write( "solve equation on interval [0,2pi) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618770 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52873)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"2%2Asin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asin%28x%29 ALIGN=MIDDLE  ALT=\"3%2Asin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let us introduce a new variable, &nbsp;y = sin(x).\r<BR>\n" );
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document.write( "Then the equation takes the form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2 ALIGN=MIDDLE  ALT=\"2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+%2B+5 ALIGN=MIDDLE  ALT=\"3y+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;&nbsp;&nbsp;&nbsp;or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2 ALIGN=MIDDLE  ALT=\"2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y ALIGN=MIDDLE  ALT=\"3y\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Solve it by using the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%2C2%5D ALIGN=MIDDLE  ALT=\"y%5B1%2C2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+%2B-+sqrt%283%5E2+%2B+4%2A2%2A5%29%29%2F4 ALIGN=MIDDLE  ALT=\"%283+%2B-+sqrt%283%5E2+%2B+4%2A2%2A5%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+%2B-+sqrt%2849%29%29%2F4 ALIGN=MIDDLE  ALT=\"%283+%2B-+sqrt%2849%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+%2B-+7%29%2F4 ALIGN=MIDDLE  ALT=\"%283+%2B-+7%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1 &nbsp;&nbsp;-----> &nbsp;&nbsp;sin(x) = -1 &nbsp;&nbsp;-----> &nbsp;&nbsp;x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Api%2F2 ALIGN=MIDDLE  ALT=\"3%2Api%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F4 ALIGN=MIDDLE  ALT=\"10%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;doesn't fit, &nbsp;because &nbsp;sin(x) &nbsp;can not be more than &nbsp;1.\r<BR>\n" );
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document.write( "<U>Answer</U>. &nbsp;x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Api%2F2 ALIGN=MIDDLE  ALT=\"3%2Api%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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