document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170891>Question 170891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help show me how to solve this quadratic equation by completing the square.\r<BR>\n" );
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document.write( "w^2 - 5w = 14\r<BR>\n" );
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document.write( "Thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126225 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=126225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+-+5w+=+14 ALIGN=MIDDLE  ALT=\"w%5E2+-+5w+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28w%29=%28w%5E2-5w%29-14 ALIGN=MIDDLE  ALT=\"f%28w%29=%28w%5E2-5w%29-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Complete the square by adding 6-1/4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28w%29=%28w%5E2-5w%2B6%281%2F4%29%29highlight%28-6%281%2F4%29%29-14 ALIGN=MIDDLE  ALT=\"f%28w%29=%28w%5E2-5w%2B6%281%2F4%29%29highlight%28-6%281%2F4%29%29-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Remember to subtract 6-1/4 too so the value of the expression does not change.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28w%29=%28w-2%281%2F2%29%29%5E2-highlight%28%2825%2F4%29%29-14 ALIGN=MIDDLE  ALT=\"f%28w%29=%28w-2%281%2F2%29%29%5E2-highlight%28%2825%2F4%29%29-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> convert to improper fractions so it's easier to deal with.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28w%29=%28w-2%281%2F2%29%29%5E2-%2825-56%29%2F4=highlight%28%28w-2%281%2F2%29%29%5E2-%2881%2F4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, ANSWER<BR>\n" );
document.write( "You know what, it follows \"vertex-form\" for a quadratic function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=w ALIGN=MIDDLE  ALT=\"x=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We have, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2%281%2F2%29 ALIGN=MIDDLE  ALT=\"h=2%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, & <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%28-81%2F4%29 ALIGN=MIDDLE  ALT=\"k=%28-81%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> VERTEX POINTS<BR>\n" );
document.write( "Let's see the graph below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-8%2C8%2C-22%2C10%2Cgrid%281%29%2Cgraph%28300%2C300%2C-8%2C8%2C-22%2C10%2Cx%5E2-5x-14%29%2Ccircle%282.5%2C-81%2F4%2C.20%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---> see vertex (2-1/2,-81/4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's see the x-intercepts:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=x ALIGN=MIDDLE  ALT=\"w=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x-14=0 ALIGN=MIDDLE  ALT=\"x%5E2-5x-14=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=1%2Cb=-5%2Cc=-14%29 ALIGN=MIDDLE  ALT=\"system%28a=1%2Cb=-5%2Cc=-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By Quadratic Eqn: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%28-5%2B-sqrt%28-5%5E2-4%2A1%2A-14%29%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-%28-5%2B-sqrt%28-5%5E2-4%2A1%2A-14%29%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%285%2B-sqrt%2825%2B56%29%29%2F2=%285%2B-sqrt%2881%29%29%2F2=%285%2B-9%29%2F2 ALIGN=MIDDLE  ALT=\"x=%285%2B-sqrt%2825%2B56%29%29%2F2=%285%2B-sqrt%2881%29%29%2F2=%285%2B-9%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=%285%2B9%29%2F2=14%2F2=highlight%287%29 ALIGN=MIDDLE  ALT=\"x=%285%2B9%29%2F2=14%2F2=highlight%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%285-9%29%2F2=-4%2F2=highlight%28-2%29 ALIGN=MIDDLE  ALT=\"x=%285-9%29%2F2=-4%2F2=highlight%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "See again the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-8%2C8%2C-22%2C10%2Cgrid%281%29%2Cgraph%28300%2C300%2C-8%2C8%2C-22%2C10%2Cx%5E2-5x-14%29%2Ccircle%282.5%2C-81%2F4%2C.20%29%2Cblue%28circle%28-2%2C0%2C.20%29%29%2Cblue%28circle%287%2C0%2C.20%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---> see the x-intercepts (-2,0) & (7,0).It's good!<BR>\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Jojo\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );