document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=421527>Question 421527</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help having trouble with my math on this one I know I cannot factor and have to use the quadratic formula to solve, I posted the problem wrong earlier.<BR>\n" );
document.write( "6x^4-7x^2+2=0<BR>\n" );
document.write( "This is what I have so far<BR>\n" );
document.write( "-(-7)+&#8730;(-7)^2-4(6)(2)/2(6)<BR>\n" );
document.write( "49+&#8730;1/12 or 49-&#8730;1/12\r<BR>\n" );
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document.write( "I am unsure if this is in its simplest form or even if my math is correct as I am having trouble checking it. Any help is greatly appreciated. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #294375 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=294375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you let y = x^2, then your equation becomes:\r<BR>\n" );
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document.write( "6y^2 - 7x + 2 = 0\r<BR>\n" );
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document.write( "this is a quadratic equation that can now be solved.\r<BR>\n" );
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document.write( "you are correct in assuming that it can't be factored, so i went to the quadratic formula.\r<BR>\n" );
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document.write( "the standard formula of a quadratic equation with the independed variable of y is:\r<BR>\n" );
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document.write( "ay^2 + by + c = 0\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "6y^2 - 7y + 2 = 0\r<BR>\n" );
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document.write( "that makes:\r<BR>\n" );
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document.write( "a = 6<BR>\n" );
document.write( "b = -7<BR>\n" );
document.write( "c = 2\r<BR>\n" );
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document.write( "from that we can derive:\r<BR>\n" );
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document.write( "2a = 12<BR>\n" );
document.write( "b^2 = 49<BR>\n" );
document.write( "4ac = 4*6*2 = 48<BR>\n" );
document.write( "b^2 - 4ac = 1\r<BR>\n" );
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document.write( "the quadratic formula using y as the independent variable states that y = (-b +/- sqrt(b^2-4ac))/2a\r<BR>\n" );
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document.write( "that becomes x = (7 +/- sqrt(1))/12 which becomes (7 +/- 1)/12.\r<BR>\n" );
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document.write( "from that we get:\r<BR>\n" );
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document.write( "y = 8/12 or y = 6/12\r<BR>\n" );
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document.write( "your solution to the equation of 6y^2 - 7y + 2 is y = 8/12 or y = 6/12\r<BR>\n" );
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document.write( "you confirm that by substituting in the original equation to see if it's true.\r<BR>\n" );
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document.write( "when y = 8/12 and when y = 6/12, the equation 6y^2 - 7y + 2 does indeed equal to 0 so the solution is good for y.\r<BR>\n" );
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document.write( "you started by making y = x^2.\r<BR>\n" );
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document.write( "you now need to go back and solve for x.\r<BR>\n" );
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document.write( "you have x^2 = 8/12 and you have x^2 = 6/12, because x^2 is equivalent to y.\r<BR>\n" );
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document.write( "this leads to x = + or - sqrt (8/12) and x = + or - sqrt (6/12).\r<BR>\n" );
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document.write( "you confirm that by substituting in your original equation of 6x^4 - 7x^2 + 2 = 0.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when x = - sqrt(8/12), the equation becomes 6 * (-sqrt(8/12)^4 - 7 * (-sqrt(8/12)^2 + 2 = 0\r<BR>\n" );
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document.write( "you can use your calculator to confirm that this becomes 6 * .4444444444 - 7 * .666666667 + 2 = 0 which becomes 0 = 0 \r<BR>\n" );
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document.write( "you need to store your intermediate results to minimize the impact of rounding.\r<BR>\n" );
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document.write( "first you take sqrt(8/12) and then make it minus and then raise it to the 4th power and then store it in memory location 1.\r<BR>\n" );
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document.write( "you will get .44444444 which, when stored, will be carried out many more decimal places.\r<BR>\n" );
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document.write( "next you take sqrt(8/12) and then make it minus and then raise it to the 2d power and then store it in memory location 2.\r<BR>\n" );
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document.write( "you will get .666666667 which, when stored, will be carried out many more decimal places.\r<BR>\n" );
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document.write( "you will then take your equation of 6x^4 - 7x^2 + 2 = 0 and translate it to:\r<BR>\n" );
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document.write( "6 * memory location 1 - 7 * memory location 2 + 2 = 0\r<BR>\n" );
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document.write( "once solved, you will see that the answer will be equal to 0, confirming your solution is correct.\r<BR>\n" );
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document.write( "the solution to your problem is x = +/- sqrt (8/12) or x = +/- sqrt (6/12).\r<BR>\n" );
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document.write( "you solved it by making y = x^2 and then solving for the quadratic equation of 6y^2 - 7y + 2 = 0\r<BR>\n" );
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document.write( "that got you y = 8/12 or y = 6/12\r<BR>\n" );
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document.write( "you then derived the final solution by taking y = x^2 and solving for x which led to x = +/0 sqrt(y).\r<BR>\n" );
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document.write( "it was hard for me to determine if that's what you did.\r<BR>\n" );
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document.write( "if so, you did it right.\r<BR>\n" );
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document.write( "if not, then you may want to re-look at the problem in light of what i just showed you.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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