document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=97624>Question 97624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP HELP HELP HELP ME PLEASE!!!!!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+x-8+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+x-8+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x-10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71041 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=71041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x+-+8%29+=+x+-+10 ALIGN=MIDDLE  ALT=\"sqrt%28x+-+8%29+=+x+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the radical on the left side by squaring both sides of the equation. On the left<BR>\n" );
document.write( "side after squaring you just have x - 8 and on the right side you square the quantity (x - 10).<BR>\n" );
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document.write( "After squaring is completed the equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+8+=+x%5E2+-+20x+%2B+100 ALIGN=MIDDLE  ALT=\"x+-+8+=+x%5E2+-+20x+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's get the equation in a more conventional form by merely switching (or transposing) <BR>\n" );
document.write( "sides ... swapping the left and right sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+20x+%2B+100+=+x+-+8 ALIGN=MIDDLE  ALT=\"x%5E2+-+20x+%2B+100+=+x+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the x on the right side by subtracting x from both sides. The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+21x+%2B+100+=+-8 ALIGN=MIDDLE  ALT=\"x%5E2+-+21x+%2B+100+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now get rid of the -8 on the right side by adding 8 to both sides. When you do that the<BR>\n" );
document.write( "equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+21x+%2B+108+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+21x+%2B+108+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is quadratic equation in a conventional form. If you play with it a little, you will <BR>\n" );
document.write( "find that it factors to become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-12%29%28x+-+9%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-12%29%28x+-+9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left side of this equation will be zero (the same as the right side) if either of the<BR>\n" );
document.write( "factors is equal to zero.<BR>\n" );
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document.write( "So possible answers come from setting each of the factors equal to zero to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+12+=+0 ALIGN=MIDDLE  ALT=\"x+-+12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which is solved by adding 12 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and another solution is obtained from setting:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+9+=+0 ALIGN=MIDDLE  ALT=\"x+-+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which can be solved by adding 9 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9 ALIGN=MIDDLE  ALT=\"x+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So we have two possible answers ... x = 12 and x = 9.<BR>\n" );
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document.write( "Check both answers by returning to the equation that you were given and substitute<BR>\n" );
document.write( "(one at a time) +12 for x and + 9 for x to see if they both work.<BR>\n" );
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document.write( "If you substitute +12 for x in the equation you were given you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812-8%29+=+12+-+10 ALIGN=MIDDLE  ALT=\"sqrt%2812-8%29+=+12+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29+=+12+-10 ALIGN=MIDDLE  ALT=\"sqrt%284%29+=+12+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this furthermore reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+2 ALIGN=MIDDLE  ALT=\"2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So this answer checks.<BR>\n" );
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document.write( "Now try letting x = 9. Substitute 9 for x in the given equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289-8%29+=+9+-+10 ALIGN=MIDDLE  ALT=\"sqrt%289-8%29+=+9+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%29+=+-1 ALIGN=MIDDLE  ALT=\"sqrt%281%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but the square root of 1 is +1 and this does not equal -1. So the answer x = 9 does not<BR>\n" );
document.write( "work out in the equation. Discard this answer. The only answer that satisfies the original<BR>\n" );
document.write( "equation is x = 12.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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