document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=640197>Question 640197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for X: &#8730;(X+5)=X-1<BR>\n" );
document.write( "(&#8730;(X+5))^2=(X-1)^2<BR>\n" );
document.write( "X+5=X^2-2X+1<BR>\n" );
document.write( "X^2-3X-4=0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403058 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=403058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Almost there! :)  Last line says: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+3x+-+4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+3x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can solve for x in 3 different ways:  factoring, completing the square, or using the quadratic formula.  The easiest of these ways is factoring, so let's see if we can factor this equation.\r<BR>\n" );
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document.write( "Let's look at the number at the end of the left side of the equal sign:  -4<BR>\n" );
document.write( "Now let's look at the middle number/variable: -3.<BR>\n" );
document.write( "For us to be able to solve by factoring, we need to have 2 numbers that multiply together to equal -4 AND can be added together to equal -3.  Let's look at the products of -4:\r<BR>\n" );
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document.write( "-1 x  4 = -4<BR>\n" );
document.write( " 1 x -4 = -4<BR>\n" );
document.write( " 2 x -2 = -4<BR>\n" );
document.write( "-2 x  2 = -4\r<BR>\n" );
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document.write( "Now, let's add each of these products to see if they equal -3:\r<BR>\n" );
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document.write( "-1 +  4 = 3<BR>\n" );
document.write( " 1 + -4 = -3\r<BR>\n" );
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document.write( "We can stop right there, because 1 + -4 = -3\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+3x+-+4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+3x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be re-written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%29%28x+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%28x+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "AND<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+4+=+0 ALIGN=MIDDLE  ALT=\"x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find out if both of these numbers are solutions, we will substitute x in our original equation for each of our possible solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B5%29+=+x+-+1 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B5%29+=+x+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%2B5%29+=+-1+%2B+-1 ALIGN=MIDDLE  ALT=\"sqrt%28-1%2B5%29+=+-1+%2B+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29+=+-2 ALIGN=MIDDLE  ALT=\"sqrt%284%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
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;\" >\r<BR>\n" );
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document.write( "Since 2 does NOT equal -2, we know that -1 is NOT a solution\r<BR>\n" );
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document.write( "Now let's try 4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B5%29+=+x+-+1 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B5%29+=+x+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2B5%29+=+4+-+1 ALIGN=MIDDLE  ALT=\"sqrt%284%2B5%29+=+4+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29+=+3 ALIGN=MIDDLE  ALT=\"sqrt%289%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+3 ALIGN=MIDDLE  ALT=\"3+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since both sides of the equal sign are the same, 4 IS a solution.  \r<BR>\n" );
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document.write( "FINAL ANSWER: x = 4 </SPAN>\n" );
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