document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088968>Question 1088968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sqrt(4x-3) = 2+sqrt(2x-5)\r<BR>\n" );
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document.write( "how to solve equations with two radicals\r<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 #703306 by </B><A HREF=/tutors/aboutme.mpl?userid=natolino_2017><B>natolino_2017(77)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=natolino_2017><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=703306\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, we need to set the restriction to allow the expression to be well defined.\r<BR>\n" );
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document.write( "4x - 3 >=0 and 2x - 5 >=0\r<BR>\n" );
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document.write( " x >= 3/4 and x>=5/2\r<BR>\n" );
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document.write( "Restriction: x>=5/2\r<BR>\n" );
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document.write( "now we solve by squaring both sides:\r<BR>\n" );
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document.write( "4x-3 = 4 +4sqrt(2x - 5) + (2x-5) \r<BR>\n" );
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document.write( "2x-2 = 4sqrt(2x-5) = 2(x-1)\r<BR>\n" );
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document.write( "(x-1) is positive according to the restriction, so we can squaring both sides\r<BR>\n" );
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document.write( "4(x^2-2x+1) = 16(2x-5)\r<BR>\n" );
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document.write( "x^2-2x+1 = 8x-20\r<BR>\n" );
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document.write( "x^2-10x+21 = 0\r<BR>\n" );
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document.write( "(x-3)(x-7) = 0\r<BR>\n" );
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document.write( "so acoording to the last expression we have 2 solution x={3,7}\r<BR>\n" );
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document.write( "but according to the restriction x>=5/2 so we don't have to discard any solution.\r<BR>\n" );
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document.write( "Final Solution={3,7}\r<BR>\n" );
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document.write( "@natolino_<BR>\n" );
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