document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622630>Question 622630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation by factorisation method x^2+(x+2)^2=650\r<BR>\n" );
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document.write( "I attempted the question but I am stuck at this step<BR>\n" );
document.write( "x^2+x^2+4-650=0<BR>\n" );
document.write( "2x^2-646=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391482 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=391482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
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document.write( "Solve the equation by factorization method.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B%28x%2B2%29%5E2=650 ALIGN=MIDDLE  ALT=\"+x%5E2%2B%28x%2B2%29%5E2=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I see one problem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%3C%3Ex%5E2%2B4 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%3C%3Ex%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You need to expand it out like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2=%28x%2B2%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2=%28x%2B2%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2=x%5E2%2B2x%2B2x%2B4 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2=x%5E2%2B2x%2B2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2=x%5E2%2B4x%2B4 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2=x%5E2%2B4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can probably take it from there, but I'll continue on just in case.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B2%29%5E2=650 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B2%29%5E2=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%5E2%2B4x%2B4%29=650 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%5E2%2B4x%2B4%29=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x-646=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x-646=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I find it much easier to factor when the leading coefficient is 1, so I will divide both sides of the equation by 2. (This step is not necessary, but it won't change the answer either.)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-323=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-323=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In order to factor this equation, we want two numbers whose product is -323 and whose sum is 2. It turns out that 17*19=323. I figured this out by checking the prime numbers (2, 3, 5, 7, 11, ...) until I found one that worked. The numbers we want are -17 and 19; their product is -323 and their sum is 2.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-323=%28x-17%29%28x%2B19%29=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-323=%28x-17%29%28x%2B19%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the product of these factors is 0, either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-17=0 ALIGN=MIDDLE  ALT=\"x-17=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B19=0 ALIGN=MIDDLE  ALT=\"x%2B19=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
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document.write( "Therefore, x=17 or x=-19.<BR>\n" );
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document.write( "It's always a good idea to check the answers in the original problem.<BR>\n" );
document.write( "x=17:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B%28x%2B2%29%5E2=650 ALIGN=MIDDLE  ALT=\"+x%5E2%2B%28x%2B2%29%5E2=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2817%29%5E2%2B%2817%2B2%29%5E2=650 ALIGN=MIDDLE  ALT=\"+%2817%29%5E2%2B%2817%2B2%29%5E2=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=289%2B361=650 ALIGN=MIDDLE  ALT=\"289%2B361=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=650=650 ALIGN=MIDDLE  ALT=\"650=650\"   DISABLED_style= \"max-width:90%; height:auto;\" > Check!!!<BR>\n" );
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document.write( "x=-19<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B%28x%2B2%29%5E2=650 ALIGN=MIDDLE  ALT=\"+x%5E2%2B%28x%2B2%29%5E2=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-19%29%5E2%2B%28-19%2B2%29%5E2=650 ALIGN=MIDDLE  ALT=\"+%28-19%29%5E2%2B%28-19%2B2%29%5E2=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=361%2B289=650 ALIGN=MIDDLE  ALT=\"361%2B289=650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=650=650 ALIGN=MIDDLE  ALT=\"650=650\"   DISABLED_style= \"max-width:90%; height:auto;\" > Check! Check!<BR>\n" );
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document.write( "Hope this helps! Feel free to email if you still have questions about this.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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