document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=903111>Question 903111</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation by introducing a substitution that transforms this equation into quadratic form.\r<BR>\n" );
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document.write( "x^4-35x^2+304=0\r<BR>\n" );
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document.write( "I'm not even sure how to begin this, but my paper has a spot for four answers if that helps? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #547799 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=547799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let some variable be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Check the discriminant to see if the quadratic equation (in quadratic form) is or is not factorable.  Solve for the variable and then solve for x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=x%5E2 ALIGN=MIDDLE  ALT=\"v=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5E2-35v%2B304=0 ALIGN=MIDDLE  ALT=\"v%5E2-35v%2B304=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >----this might be all you need as your answer, OR\r<BR>\n" );
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document.write( "... <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=discrim=35%5E2-4%2A304=9 ALIGN=MIDDLE  ALT=\"discrim=35%5E2-4%2A304=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so you should be able to FACTOR the quadratic expression.\r<BR>\n" );
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document.write( "Look at 304.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=304=2%2A152=2%2A2%2A76=2%2A2%2A2%2A2%2A38=2%2A2%2A2%2A2%2A2%2A19 ALIGN=MIDDLE  ALT=\"304=2%2A152=2%2A2%2A76=2%2A2%2A2%2A2%2A38=2%2A2%2A2%2A2%2A2%2A19\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but another way is to look for all of the two-factor factorizations of 304.<BR>\n" );
document.write( "More comfortable might be just use the general solution to find v...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=%2835%2B-+sqrt%289%29%29%2F2 ALIGN=MIDDLE  ALT=\"v=%2835%2B-+sqrt%289%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=%2835%2B-+3%29%2F2 ALIGN=MIDDLE  ALT=\"v=%2835%2B-+3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=16%29 ALIGN=MIDDLE  ALT=\"highlight%28v=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=19%29 ALIGN=MIDDLE  ALT=\"highlight%28v=19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now find x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-sqrt%2819%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-sqrt%2819%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=sqrt%2819%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x=sqrt%2819%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Like just said, if you do not yet know about the general solution you CAN factor the quadratic expression; it just requires looking for the right two factors for 304. </SPAN>\n" );
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