document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360579>Question 360579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve this equation by using the quadratic form.<BR>\n" );
document.write( "x(1/2) + (sqrt 3)x(1/4) - 18 = 0<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x to the 1/2 power plus sqrt of 3 x to the 1/4 power - 18 = 0.\r<BR>\n" );
document.write( "\n" );
document.write( "Any help will be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257294 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=257294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x(1/2) + (sqrt 3)x(1/4) - 18 = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Let w = x^(1/4)<BR>\n" );
document.write( "Then w^2 = x^(1/2)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Substitute to get:<BR>\n" );
document.write( "w^2 + sqrt(3)w - 18 = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Quadratic Formula:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "w = [-sqrt(3) +- sqrt(3-4*-18)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "w = [-sqrt(3) +- sqrt(75)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "w = [-sqrt(3)+-5sqrt(3)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "w = [-3sqrt(3)] or w = 2sqrt(3)<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Now, solve for \"x\" using Let w = x^(1/4)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Solve: -3sqrt(3) = x^(1/4)<BR>\n" );
document.write( "x = [-3sqrt(3)]^4 = 81*9 = 729<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Solve: 2sqrt(3) = x^(1/4)<BR>\n" );
document.write( "x = [2sqrt(3)]^4 = 16*9 = 144<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Check these answers in the original equation:<BR>\n" );
document.write( "========<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );