document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133599>Question 133599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a value for k that will make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B12x%2Bk ALIGN=MIDDLE  ALT=\"4x%5E2%2B12x%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > a perfect square.  Describe the procedure that you used which requires algebra (this is not a trial and error). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97758 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1: Divide the entire polynomial by the coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x%2Bk%2F4 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x%2Bk%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2: Divide the coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > term by 2:  Result: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3: Square the result of step 2:  Result: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F4 ALIGN=MIDDLE  ALT=\"9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The result of step 3 is the value of the constant term required to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x%2Bk%2F4 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x%2Bk%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > a perfect square, therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2F4=9%2F4 ALIGN=MIDDLE  ALT=\"k%2F4=9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=9 ALIGN=MIDDLE  ALT=\"k=9\"   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=x%5E2%2B3x%2B9%2F4 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x%2B9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be multiplied by 4 to reverse the effects of step 1, resulting in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B12x%2B9 ALIGN=MIDDLE  ALT=\"4x%5E2%2B12x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which then factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%282x%2B3%29=%282x%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%282x%2B3%29=%282x%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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