document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040895>Question 1040895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all values of $p$ such that$$2(x+4)(x-2p)$$has a minimum value of $-18$ over all real values of $x$. (In other words, we cannot have $x$ be nonreal.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655875 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The x-value that will give the minimum value will just be the average of the two roots, namely -4 and 2p.  Their average is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2B2p%29%2F2+=+p-2 ALIGN=MIDDLE  ALT=\"%28-4%2B2p%29%2F2+=+p-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28p-2%2B4%29%28p-2-2p%29+=+-18 ALIGN=MIDDLE  ALT=\"2%28p-2%2B4%29%28p-2-2p%29+=+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "after direct substitution into the equation.\r<BR>\n" );
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document.write( "<===> (p+2)(-p-2) = -9  <===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B2%29%5E2+=+9 ALIGN=MIDDLE  ALT=\"%28p%2B2%29%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > ===> p+2 = 3, or p+2 = -3\r<BR>\n" );
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document.write( "==> p = 1, or p = -5. </SPAN>\n" );
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