document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=14028>Question 14028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions of the equations.<BR>\n" );
document.write( "1.<BR>\n" );
document.write( "x<sup>6</sup> - 64 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "2.<BR>\n" );
document.write( "9x<sup>4</sup> - 24x<sup>3</sup> + 16x<sup>2</sup> = 0\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7046 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=7046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face = \"courier new\" size = 3><b> <BR>\n" );
document.write( "Find all solutions of the equations.<BR>\n" );
document.write( "1.<BR>\n" );
document.write( "`<BR>\n" );
document.write( "x<sup>6</sup> - 64 = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "First factor as the difference of squares.<BR>\n" );
document.write( "`<BR>\n" );
document.write( "(x<sup>3</sup>)<sup>2</sup> - 8<sup>2</sup> = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "(x<sup>3</sup> - 8)(x<sup>3</sup> + 8) = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Next factor these two parenthetical expressiona as the difference and<BR>\n" );
document.write( "sum respectively of two cubes<BR>\n" );
document.write( "`<BR>\n" );
document.write( "(x<sup>3</sup> - 2<sup>3</sup>)(x<sup>3</sup> + 2<sup>3</sup>) = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "(x - 2)(x<sup>2</sup> + 2x + 4)(x + 2)(x<sup>2</sup> - 2x + 4) = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Set each of the four factors = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "x - 2 = 0, solving gives x = 2  <BR>\n" );
document.write( "` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` _<BR>\n" );
document.write( "x<sup>2</sup> + 2x + 4 = 0, solving by the quadratic formula gives x = -1±<font face = \"symbol\">Ö</font>3<BR>\n" );
document.write( "`<BR>\n" );
document.write( "x + 2 = 0, solving gives x = -2  <BR>\n" );
document.write( "` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `_<BR>\n" );
document.write( "x<sup>2</sup> - 2x + 4 = 0, solving by the quadratic formula gives x = 1±<font face = \"symbol\">Ö</font>3<BR>\n" );
document.write( "`<BR>\n" );
document.write( "-----------------------------------------------<BR>\n" );
document.write( "`<BR>\n" );
document.write( "2.<BR>\n" );
document.write( "`<BR>\n" );
document.write( "9x<sup>4</sup> - 24x<sup>3</sup> + 16x2 = 0 <BR>\n" );
document.write( "`<BR>\n" );
document.write( "Factor out x<sup>2</sup><BR>\n" );
document.write( "`<BR>\n" );
document.write( "x<sup>2</sup>(9x<sup>2</sup> - 24x + 16) = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Factor the expression in parentheses<BR>\n" );
document.write( "`<BR>\n" );
document.write( "x<sup>2</sup>(3x - 4)(3x - 4) = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "x<sup>2</sup>(3x -4)<sup>2</sup> = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Set each factor equal to 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "x<sup>2</sup> = 0 gives x = 0<BR>\n" );
document.write( "`<BR>\n" );
document.write( "(3x - 4)<sup>2</sup> = 0, gives x = 4/3<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Edwin </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );