document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224409>Question 224409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "if 2x^2 - 14x + 29 = p(x+q)^2 +r holds for all real values of x, find the values of p,q and r. Hence, state the minimum value of the function and the corresponding value of x..\r<BR>\n" );
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document.write( "im stuck.. plz help :( </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167637 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=167637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if 2x^2 - 14x + 29 = p(x+q)^2 +r holds for all real values of x, find the values of p,q and r. Hence, state the minimum value of the function and the corresponding value of x.. <BR>\n" );
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document.write( "2x^2 - 14x + 29 = px^2 + 2pqx +pq^2 +r<BR>\n" );
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document.write( "Matching up the coefficients you get:<BR>\n" );
document.write( "p = 2<BR>\n" );
document.write( "2pq= -14<BR>\n" );
document.write( "pq^2+r = 29<BR>\n" );
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document.write( "So:<BR>\n" );
document.write( "p = 2 <BR>\n" );
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document.write( "q = (14/4) = 7/2<BR>\n" );
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document.write( "2(7/2)^2+r = 29<BR>\n" );
document.write( "(49/2) + r = (58/2)<BR>\n" );
document.write( "r = 9/2<BR>\n" );
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document.write( "Hence, state the minimum value of the function and the corresponding value of x<BR>\n" );
document.write( "a = 2 ; b = -14<BR>\n" );
document.write( "min occurs at x = -b/2a = 14/4 = 7/2<BR>\n" );
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document.write( "2x^2 - 14x + 29 <BR>\n" );
document.write( "Minimum value is 2(29)^2 - 14*29 +29 = 1305<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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