document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=609539>Question 609539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for the value of x of arctan(3 + 4x = x^2) = -pi/4\r<BR>\n" );
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document.write( "please if you can help me solve this I have no idea what to do. our prof only ever gives us examples like y = sin (-1/2) and honestly I don't know what to do with whatever information I can squeeze out of that simple example to solve something as complicated as this homework.\r<BR>\n" );
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document.write( "If you can also explain the steps that'd be really great. Thank you to anyone who answers this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #383779 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=383779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume that the equation is<BR>\n" );
document.write( "arctan(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4x+%2B+x%5E2 ALIGN=MIDDLE  ALT=\"3+%2B+4x+%2B+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pi%2F4 ALIGN=MIDDLE  ALT=\"-pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "arctan(something) represents \"an angle whose tan ratio is 'something'\". So <BR>\n" );
document.write( "arctan(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4x+%2B+x%5E2 ALIGN=MIDDLE  ALT=\"3+%2B+4x+%2B+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "represents an angle whose tan ratio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4x+%2B+x%5E2 ALIGN=MIDDLE  ALT=\"3+%2B+4x+%2B+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "And the equation<BR>\n" );
document.write( "arctan(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4x+%2B+x%5E2 ALIGN=MIDDLE  ALT=\"3+%2B+4x+%2B+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pi%2F4 ALIGN=MIDDLE  ALT=\"-pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "tells us that this angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pi%2F4 ALIGN=MIDDLE  ALT=\"-pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We should know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28-pi%2F4%29+=+-1 ALIGN=MIDDLE  ALT=\"tan%28-pi%2F4%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28-pi%2F4%29+=+-1 ALIGN=MIDDLE  ALT=\"tan%28-pi%2F4%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since the equation arctan(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4x+%2B+x%5E2 ALIGN=MIDDLE  ALT=\"3+%2B+4x+%2B+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pi%2F4 ALIGN=MIDDLE  ALT=\"-pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells us that the tan of the same angle is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4x%2Bx%5E2 ALIGN=MIDDLE  ALT=\"3+%2B+4x%2Bx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4x-x%5E2 ALIGN=MIDDLE  ALT=\"3+%2B+4x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and -1 must be equal to each other. Now we just have to solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4x%2Bx%5E2+=+-1 ALIGN=MIDDLE  ALT=\"3+%2B+4x%2Bx%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since this is a quadratic equation we want one side to be zero. Adding 1 to each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+4x%2Bx%5E2+=+0 ALIGN=MIDDLE  ALT=\"4+%2B+4x%2Bx%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we factor (or use the Quadratic Formula). To make the factoring easier, I'm going to rearrange the terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+%2B+4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+%2B+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This factors easily into:<BR>\n" );
document.write( "(x+2)(x+2) = 0<BR>\n" );
document.write( "From the Zero Product Property we know that one or more of the factors must be zero. So<BR>\n" );
document.write( "x + 2 = 0<BR>\n" );
document.write( "Solving we get<BR>\n" );
document.write( "x = -2 </SPAN>\n" );
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