document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150082>Question 1150082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of x that makes the following equation true:\r<BR>\n" );
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document.write( "Equation: https://imgur.com/a/jiqbd9p </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771444 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=771444\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "Problem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/4nXUmA9.jpg\" width = \"200\">\r<BR>\n" );
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document.write( "The given equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283x%29+%2B+sqrt%283%2Fx%29+-+2sqrt%283%29%29%2F%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%29+=+%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%29%2F%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%2Bsqrt%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "has the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%29+%2B+sqrt%283%2Fx%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%29+%2B+sqrt%283%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > show up a bunch of times as shown by the red marker\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28red%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%29+-+2sqrt%283%29%29%2F%28red%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%29%29+=+%28red%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%29%29%2F%28red%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%29%2Bsqrt%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we can replace every copy of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%29+%2B+sqrt%283%2Fx%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%29+%2B+sqrt%283%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with some other variable temporarily. Lets call that y.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%283x%29+%2B+sqrt%283%2Fx%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%283x%29+%2B+sqrt%283%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The given equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283x%29+%2B+sqrt%283%2Fx%29+-+2sqrt%283%29%29%2F%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%29+=+%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%29%2F%28sqrt%283x%29+%2B+sqrt%283%2Fx%29%2Bsqrt%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplifies greatly to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+2sqrt%283%29%29%2F%28y%29+=+%28y%29%2F%28y%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28y+-+2sqrt%283%29%29%2F%28y%29+=+%28y%29%2F%28y%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Recall that the range of the square root function is nonnegative. In other words, it is impossible to get a negative value output from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Adding two nonnegative square roots in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%283x%29+%2B+sqrt%283%2Fx%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%283x%29+%2B+sqrt%283%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E+0 ALIGN=MIDDLE  ALT=\"y+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We'll use this fact later.\r<BR>\n" );
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document.write( "Let's solve for y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+2sqrt%283%29%29%2F%28y%29+=+%28y%29%2F%28y%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28y+-+2sqrt%283%29%29%2F%28y%29+=+%28y%29%2F%28y%2Bsqrt%283%29%29\"   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=%28y+-+2sqrt%283%29%29%28y%2Bsqrt%283%29%29+=+y%2Ay ALIGN=MIDDLE  ALT=\"%28y+-+2sqrt%283%29%29%28y%2Bsqrt%283%29%29+=+y%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+2sqrt%283%29%29%28y%2Bsqrt%283%29%29+=+y%5E2 ALIGN=MIDDLE  ALT=\"%28y+-+2sqrt%283%29%29%28y%2Bsqrt%283%29%29+=+y%5E2\"   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=A%28y%2Bsqrt%283%29%29+=+y%5E2 ALIGN=MIDDLE  ALT=\"A%28y%2Bsqrt%283%29%29+=+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Temporarily, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28y+-+2sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"A+=+%28y+-+2sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This helps us distribute in the next step\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2Ay+%2B+A%2Asqrt%283%29+=+y%5E2 ALIGN=MIDDLE  ALT=\"A%2Ay+%2B+A%2Asqrt%283%29+=+y%5E2\"   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=y%2AA+%2B+sqrt%283%29%2AA+=+y%5E2 ALIGN=MIDDLE  ALT=\"y%2AA+%2B+sqrt%283%29%2AA+=+y%5E2\"   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=y%28y+-+2sqrt%283%29%29%2Bsqrt%283%29%28y+-+2sqrt%283%29%29+=+y%5E2 ALIGN=MIDDLE  ALT=\"y%28y+-+2sqrt%283%29%29%2Bsqrt%283%29%28y+-+2sqrt%283%29%29+=+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace A with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+2sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28y+-+2sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > again.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28y%29+%2B+y%28-2sqrt%283%29%29%2Bsqrt%283%29%28y%29+%2B+sqrt%283%29%2A%28-2sqrt%283%29%29+=+y%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute again\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+2y%2Asqrt%283%29+%2B+y%2Asqrt%283%29-6+=+y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2+-+2y%2Asqrt%283%29+%2B+y%2Asqrt%283%29-6+=+y%5E2\"   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=y%5E2+-+y%2Asqrt%283%29-6+=+y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2+-+y%2Asqrt%283%29-6+=+y%5E2\"   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=y%5E2+-+y%2Asqrt%283%29-6-y%5E2+=+y%5E2-y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2+-+y%2Asqrt%283%29-6-y%5E2+=+y%5E2-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract y^2 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%2Asqrt%283%29-6+=+0 ALIGN=MIDDLE  ALT=\"-y%2Asqrt%283%29-6+=+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=-y%2Asqrt%283%29-6%2By%2Asqrt%283%29+=+0%2By%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"-y%2Asqrt%283%29-6%2By%2Asqrt%283%29+=+0%2By%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add y*sqrt(3) to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+y%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"-6+=+y%2Asqrt%283%29\"   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=y%2Asqrt%283%29+=+-6 ALIGN=MIDDLE  ALT=\"y%2Asqrt%283%29+=+-6\"   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=%28y%2Asqrt%283%29%29%2F%28sqrt%283%29%29+=+-6%2F%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28y%2Asqrt%283%29%29%2F%28sqrt%283%29%29+=+-6%2F%28sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by sqrt(3)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6%2F%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"y+=+-6%2F%28sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by sqrt(3)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3.46410161513776 ALIGN=MIDDLE  ALT=\"y+=+-3.46410161513776\"   DISABLED_style= \"max-width:90%; height:auto;\" > we've run into a problem\r<BR>\n" );
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document.write( "The result we got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3.46410161513776 ALIGN=MIDDLE  ALT=\"y+=+-3.46410161513776\"   DISABLED_style= \"max-width:90%; height:auto;\" > contradicts <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E+0 ALIGN=MIDDLE  ALT=\"y+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There are no solutions for y, which means that <font color=red size=4>there are no solutions for x</font>.<BR>\n" );
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