document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185592>Question 185592</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Two positive real numbers have a sum of 7 and a product of 11. Find the numbers.<BR>\n" );
document.write( "I don't know how to start this problem. \r<BR>\n" );
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document.write( "Also. 2x^2 + 6x + 3 = 0<BR>\n" );
document.write( "how would you do this using completing the square? I did it. but ended up with a weird answer like -3/2 +or-  the square root of 3 over 2.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139222 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=139222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two positive real numbers be x and y, then...<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By+=+7 ALIGN=MIDDLE  ALT=\"x%2By+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"Two positive real numbers have a sum of 7...\"<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay+=+11 ALIGN=MIDDLE  ALT=\"x%2Ay+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"...and a product of 11.\"<BR>\n" );
document.write( "Rewrite equation 1) as x = 7-y and substitute this for x in equation 2)<BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-y%29%2Ay+=+11 ALIGN=MIDDLE  ALT=\"%287-y%29%2Ay+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Perform the indicated multiplication (distribute) on the left side.<BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y-y%5E2+=+11 ALIGN=MIDDLE  ALT=\"7y-y%5E2+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange to form a standard quadratic equation.<BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-7y%2B11+=+0 ALIGN=MIDDLE  ALT=\"y%5E2-7y%2B11+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve (a = 1, b = -7, c = 11):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-7%29%2B-sqrt%28%28-7%29%5E2-4%281%29%2811%29%29%29%2F2%281%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-7%29%2B-sqrt%28%28-7%29%5E2-4%281%29%2811%29%29%29%2F2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%287%2B-sqrt%2849-44%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%287%2B-sqrt%2849-44%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%287%2B-sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%287%2B-sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+%287%2Bsqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+%287%2Bsqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+%287-sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+%287-sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%287%2Bsqrt%285%29%29%2F2%29%2B%28%287-sqrt%285%29%29%2F2%29+=+%2814%2Bsqrt%285%29-sqrt%285%29%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F2+=+7 ALIGN=MIDDLE  ALT=\"14%2F2+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%287%2Bsqrt%285%29%29%2F2%29%2A%28%287-sqrt%285%29%29%2F2%29+=+%2849-5%29%2F4 ALIGN=MIDDLE  ALT=\"%28%287%2Bsqrt%285%29%29%2F2%29%2A%28%287-sqrt%285%29%29%2F2%29+=+%2849-5%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44%2F4+=+11 ALIGN=MIDDLE  ALT=\"44%2F4+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On part 2 of the problem, your \"weird\" answer is the correct solution!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+%28-3%2F2%29%2Bsqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+%28-3%2F2%29%2Bsqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+%28-3%2F2%29-sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+%28-3%2F2%29-sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );