document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177920>Question 177920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Algebraically find the EXACT ROOTS in simplest form for: x/-7=(x+1)/(x-11) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132959 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=132959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this equation doesn't have any roots.<BR>\n" );
document.write( "when you solve for the roots you get a complex number.<BR>\n" );
document.write( "complex number means there are no roots.<BR>\n" );
document.write( "here's how i did it.<BR>\n" );
document.write( "your equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F-7%29+=+%28x%2B1%29%2F%28x-11%29 ALIGN=MIDDLE  ALT=\"%28x%2F-7%29+=+%28x%2B1%29%2F%28x-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "muiltiply both sides by -7 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7+%2A+%28x%2B1%29%2F%28x-11%29 ALIGN=MIDDLE  ALT=\"x+=+-7+%2A+%28x%2B1%29%2F%28x-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by (x-11) to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2A+%28x-11%29+=+-7+%2A+%28x%2B1%29 ALIGN=MIDDLE  ALT=\"x+%2A+%28x-11%29+=+-7+%2A+%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+11x+=+-7x+-+7 ALIGN=MIDDLE  ALT=\"x%5E2+-+11x+=+-7x+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 7x to both sides to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+11x+%2B+7x+=+-7 ALIGN=MIDDLE  ALT=\"x%5E2+-+11x+%2B+7x+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 7 to both sides to get\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+11x+%2B+7x+%2B+7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+11x+%2B+7x+%2B+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4x+%2B+7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+%2B+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you can solve this using the quadratic formula or completing the squares.<BR>\n" );
document.write( "either way will get you the same answer.<BR>\n" );
document.write( "i'll use the quadratic formula first:<BR>\n" );
document.write( "a = 1 = coefficient of the x^2 term.<BR>\n" );
document.write( "b = -4 = coefficient of the x term.<BR>\n" );
document.write( "c = 7 = constant term.<BR>\n" );
document.write( "quadratic formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%2F%282a%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%2F%282a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting values for a,b,c gets:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-4%29+%2B-+sqrt%28%28-4%29%5E2+-+4%2A7%2A1%29%2F%282%2A1%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-4%29+%2B-+sqrt%28%28-4%29%5E2+-+4%2A7%2A1%29%2F%282%2A1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4+%2B-+sqrt%2816+-+28%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+4+%2B-+sqrt%2816+-+28%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4+%2B-+sqrt%28-12%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+4+%2B-+sqrt%28-12%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4+%2B-+sqrt%28-3%2A2%2A2%29+%2F+%282%29+ ALIGN=MIDDLE  ALT=\"x+=+4+%2B-+sqrt%28-3%2A2%2A2%29+%2F+%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+%2B-+2%2Asqrt%28-3%29%2F%282%29 ALIGN=MIDDLE  ALT=\"+x+=+4+%2B-+2%2Asqrt%28-3%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2+%2B-+sqrt%28-3%29 ALIGN=MIDDLE  ALT=\"+x+=+2+%2B-+sqrt%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you can also solve this by completing the squares as follows:<BR>\n" );
document.write( "your equation after manipulating it is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4x+%2B+7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+%2B+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is the same place where we solved it using the quadratic formula.<BR>\n" );
document.write( "this time, however, we will complete the squares.<BR>\n" );
document.write( "subtract 7 from both sides to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4x+=+-7 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+=+-7\"   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+-+4x+=+%28x-2%29%5E2+-+4 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+=+%28x-2%29%5E2+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "your equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2+-+4+=+-7 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2+-+4+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you add 4 to both sides to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2+=+-3 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you take the square root of both sides to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2 ALIGN=MIDDLE  ALT=\"x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-3%29 ALIGN=MIDDLE  ALT=\"sqrt%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you add 2 to both sides to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2+%2B-+sqrt%28-3%29 ALIGN=MIDDLE  ALT=\"x+=+2+%2B-+sqrt%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "since the value of x is a complex number, this means that there are no roots to the equation.<BR>\n" );
document.write( "since the roots are when the equation crosses the x-axis, this means that this equation does not cross the x-axis.<BR>\n" );
document.write( "a graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B7 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-20%2C20%2C-20%2C20%2Cx%5E2-4x%2B7%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C800%2C-20%2C20%2C-20%2C20%2Cx%5E2-4x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );