document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314432>Question 314432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CAN YOU PLEASE HELP ME FIND THE CORRESPONDING SQAURE ROOTS OF THIS PROBLEM? <BR>\n" );
document.write( "3x^2-2=4x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224828 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=224828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a quadratic equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The roots of this quadratic equation need to be found using the quadratic formula or the completing the squares method.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factoring will not do it because the roots are not integers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The quadratic formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your formula starts out as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+2+=+4x ALIGN=MIDDLE  ALT=\"3x%5E2+-+2+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract 4x from both sides of this equation to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+4x+-+2+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+-+4x+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now the equation is in the standard form of a quadratic equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The standard form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In your equation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a = 3<BR>\n" );
document.write( "b = -4<BR>\n" );
document.write( "c = -2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In the quadratic formula, this makes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-b = 4<BR>\n" );
document.write( "2a = 6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%5E2-4ac%29 ALIGN=MIDDLE  ALT=\"sqrt%28b%5E2-4ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-4%29%5E2+-+%284%2A3%2A%28-2%29%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-4%29%5E2+-+%284%2A3%2A%28-2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2840%29 ALIGN=MIDDLE  ALT=\"sqrt%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.32455532\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Placing these values into the quadratic formula gets you:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 1.72075922 and x = -.387425887\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Those are your roots.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You confirm by replacing x in your original equation with these values to determine if the equations are true or not.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When you replace x with -.387425887, your original equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3*(-.387425887)^2 - 4*(-.387425887) - 2 = 0 which simplifies to:<BR>\n" );
document.write( ".450296453 - (1.549703547) - 2 = 0 which simplifies to:<BR>\n" );
document.write( "2 - 2 = 0 which is true, confirming that the value of x = -.387425887 is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );