document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85836>Question 85836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the square root of 2x plus three minus the square root ofx plus one  equals one </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62052 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=62052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the square root of 2x plus three minus the square root ofx plus one equals one<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Here it is step-by-step, the idea is to perform algebra operations that will get rid of the radicals; Leaving us with a quadratic equation that we solve<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x+%2B+3%29 ALIGN=MIDDLE  ALT=\"sqrt%282x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x+%2B+3%29 ALIGN=MIDDLE  ALT=\"sqrt%282x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Square both sides:<BR>\n" );
document.write( "2x + 3 = (x+1) + 2*sqrt(x+1) + 1; FOILed [(sqrt(x+1) + 1] * [sqrt(x+1) + 1]<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2x + 3 = x + 2 + 2*sqrt(x+1)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2x - x + 3 - 2 = 2*sqrt(x+1)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x + 1 = 2*Sqrt(x+1)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Square both sides again:<BR>\n" );
document.write( "x^2 + 2x + 1 = 4(x+1); FOILed (x+1)*(x+1)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x^2 + 2x + 1 = 4x + 4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x^2 + 2x - 4x + 1 - 4 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x^2 - 2x - 3 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(x - 3)(x + 1 ) = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x = +3<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = -1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check both solutions by substitution in the original equation. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );