document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=264629>Question 264629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete the square,simplify. Express any complex numbers using i notation\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5x-9=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(2x  )(x  )\r<BR>\n" );
document.write( "\n" );
document.write( "I am stuck because I can not figure out which 2 numbers multiply to 9 and add to 5.If I use (2x+3)(x+1) I can get 5x but no 9. Please help! This is where I always get stuck while factoring. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194788 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=194788\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It turns out that you can't factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5x-9 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > over the rationals. So let's follow the instructions and complete the square.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5x-9 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2%2B%285%2F2%29x-9%2F2%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2%2B%285%2F2%29x-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out 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;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This step is very important: 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;\" > coefficient <font size=4><b>must</b></font> be equal to 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take half of 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;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%285%2F2%29=5%2F4 ALIGN=MIDDLE  ALT=\"%281%2F2%29%285%2F2%29=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F16 ALIGN=MIDDLE  ALT=\"25%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F4%29%5E2=%285%2F4%29%285%2F4%29=25%2F16 ALIGN=MIDDLE  ALT=\"%285%2F4%29%5E2=%285%2F4%29%285%2F4%29=25%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2%2B%285%2F2%29x%2Bhighlight%2825%2F16-25%2F16%29-9%2F2%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2%2B%285%2F2%29x%2Bhighlight%2825%2F16-25%2F16%29-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add <font size=4><b>and</b></font> subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F16 ALIGN=MIDDLE  ALT=\"25%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > inside the parenthesis. Make sure to place this after the \"x\" term. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F16-25%2F16=0 ALIGN=MIDDLE  ALT=\"25%2F16-25%2F16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the expression is not changed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%28x%5E2%2B%285%2F2%29x%2B25%2F16%29-25%2F16-9%2F2%29 ALIGN=MIDDLE  ALT=\"2%28%28x%5E2%2B%285%2F2%29x%2B25%2F16%29-25%2F16-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the first three terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%28x%2B5%2F4%29%5E2-25%2F16-9%2F2%29 ALIGN=MIDDLE  ALT=\"2%28%28x%2B5%2F4%29%5E2-25%2F16-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%285%2F2%29x%2B25%2F16 ALIGN=MIDDLE  ALT=\"x%5E2%2B%285%2F2%29x%2B25%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%28x%2B5%2F4%29%5E2-97%2F16%29 ALIGN=MIDDLE  ALT=\"2%28%28x%2B5%2F4%29%5E2-97%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F4%29%5E2%2B2%28-97%2F16%29 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F4%29%5E2%2B2%28-97%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F4%29%5E2-97%2F8 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F4%29%5E2-97%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So after completing the square, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5x-9 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > transforms to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F4%29%5E2-97%2F8 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F4%29%5E2-97%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5x-9=2%28x%2B5%2F4%29%5E2-97%2F8 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x-9=2%28x%2B5%2F4%29%5E2-97%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5x-9=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F4%29%5E2-97%2F8=0 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F4%29%5E2-97%2F8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F4%29%5E2-97%2F8=0 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F4%29%5E2-97%2F8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F4%29%5E2-97%2F8=0 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F4%29%5E2-97%2F8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F4%29%5E2=0%2B97%2F8 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F4%29%5E2=0%2B97%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=97%2F8 ALIGN=MIDDLE  ALT=\"97%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F4%29%5E2=97%2F8 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F4%29%5E2=97%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F4%29%5E2=%2897%2F8%29%2F%282%29 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F4%29%5E2=%2897%2F8%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F4%29%5E2=97%2F16 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F4%29%5E2=97%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F4=%22%22%2B-sqrt%2897%2F16%29 ALIGN=MIDDLE  ALT=\"x%2B5%2F4=%22%22%2B-sqrt%2897%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F4=sqrt%2897%2F16%29 ALIGN=MIDDLE  ALT=\"x%2B5%2F4=sqrt%2897%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F4=-sqrt%2897%2F16%29 ALIGN=MIDDLE  ALT=\"x%2B5%2F4=-sqrt%2897%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the \"plus/minus\" to form two equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F4=sqrt%2897%29%2F4 ALIGN=MIDDLE  ALT=\"x%2B5%2F4=sqrt%2897%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F4=-sqrt%2897%29%2F4 ALIGN=MIDDLE  ALT=\"x%2B5%2F4=-sqrt%2897%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify the square root.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F4%2Bsqrt%2897%29%2F4 ALIGN=MIDDLE  ALT=\"x=-5%2F4%2Bsqrt%2897%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F4-sqrt%2897%29%2F4 ALIGN=MIDDLE  ALT=\"x=-5%2F4-sqrt%2897%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-5%2Bsqrt%2897%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%28-5%2Bsqrt%2897%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-5-sqrt%2897%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%28-5-sqrt%2897%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-5%2Bsqrt%2897%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%28-5%2Bsqrt%2897%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-5-sqrt%2897%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%28-5-sqrt%2897%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );