document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60914>Question 60914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I can only solve part of this equation and then I get stuck.  Can someone show me the next steps I need to take and explain how they are done? I have done the equation as far as I can:\r<BR>\n" );
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document.write( "SQRT(2X-1)+SQRT(X-4)= 4   <----original equation\r<BR>\n" );
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document.write( "SQRT(2X-1)=4-SQRT(X-4)<BR>\n" );
document.write( "(SQRT<2X-1>)^2 = (4-SQRT<X-4>)^2<BR>\n" );
document.write( "2X-1 = (4-SQRT<X-4>)(4-SQRT<X-4>)  <------I am lost as to how to solve finish this side of the equation.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41869 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><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=41869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation to solve is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x-1%29%2Bsqrt%28x-4%29=4 ALIGN=MIDDLE  ALT=\"sqrt%282x-1%29%2Bsqrt%28x-4%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This is a quadratic equation in disguise!<BR>\n" );
document.write( "The trick to solving these is to get all the square root stuff onto one side of the equation then square both sides. Then, you're left with a quadratic equation to solve:\r<BR>\n" );
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document.write( "Square both sides of the equation to solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x-1%29%29%5E2+%2B+sqrt%28x-4%29%5E2+=+4%5E2+=+16 ALIGN=MIDDLE  ALT=\"%28sqrt%282x-1%29%29%5E2+%2B+sqrt%28x-4%29%5E2+=+4%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This expands to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29%2B%28x-4%29%2B2sqrt%28%282x-1%29%28x-4%29%29+=+16 ALIGN=MIDDLE  ALT=\"%282x-1%29%2B%28x-4%29%2B2sqrt%28%282x-1%29%28x-4%29%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Collect like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-5%2B2sqrt%28%282x-1%29%28x-4%29%29+=+16 ALIGN=MIDDLE  ALT=\"3x-5%2B2sqrt%28%282x-1%29%28x-4%29%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 16 from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-21%2B2sqrt%28%282x-1%29%28x-4%29%29+=+0 ALIGN=MIDDLE  ALT=\"3x-21%2B2sqrt%28%282x-1%29%28x-4%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28%282x-1%29%28x-4%29%29 ALIGN=MIDDLE  ALT=\"2sqrt%28%282x-1%29%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-21+=+-+2sqrt%28%282x-1%29%28x-4%29%29 ALIGN=MIDDLE  ALT=\"3x-21+=+-+2sqrt%28%282x-1%29%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, square both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-21%29%5E2+=+%28-2sqrt%28%282x-1%29%28x-4%29%29%29%5E2 ALIGN=MIDDLE  ALT=\"%283x-21%29%5E2+=+%28-2sqrt%28%282x-1%29%28x-4%29%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply things out:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-126x%2B441+=+4%282x-1%29%28x-4%29 ALIGN=MIDDLE  ALT=\"9x%5E2-126x%2B441+=+4%282x-1%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-126x%2B441+=+4%282x%5E2-9x%2B4%29+=+8x%5E2-36x%2B16 ALIGN=MIDDLE  ALT=\"9x%5E2-126x%2B441+=+4%282x%5E2-9x%2B4%29+=+8x%5E2-36x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2 ALIGN=MIDDLE  ALT=\"8x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-126x%2B441=-36x%2B16 ALIGN=MIDDLE  ALT=\"x%5E2-126x%2B441=-36x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 16 from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-126x%2B425=-36x ALIGN=MIDDLE  ALT=\"x%5E2-126x%2B425=-36x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 36x to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-90x%2B425=0 ALIGN=MIDDLE  ALT=\"x%5E2-90x%2B425=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a quadratic equation that you can solve with the quadratic formula or by factoring the equation if you can see the factors:\r<BR>\n" );
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document.write( "The equation factors into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-85%29%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-85%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The roots of the equation are 85 and 5\r<BR>\n" );
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document.write( "If you plug 85 into your original equation it doesn't work but 5 does so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is your answer. </SPAN>\n" );
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