document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=352106>Question 352106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to find all real solutions for the following equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29sqrt%28x%2B3%29=%28x%2B3%29%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%29sqrt%28x%2B3%29=%28x%2B3%29%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I converted the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B3%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F2%29%2B3%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F2%29%2B3%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the equation turned into:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%28x%5E%281%2F2%29%2B3%5E%281%2F2%29%29=%28x%2B3%29%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"x%5E2%28x%5E%281%2F2%29%2B3%5E%281%2F2%29%29=%28x%2B3%29%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then I distributed x^2 on one side and ^3/2 on the other. So I get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3x=x%5E%283%2F2%29%2B3sqrt%283%29 ALIGN=MIDDLE  ALT=\"x%2B3x=x%5E%283%2F2%29%2B3sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x and 3x can simplify to 4x. and I move this over into the other side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%283%2F2%29-4x%2B3sqrt%283%29=0 ALIGN=MIDDLE  ALT=\"x%5E%283%2F2%29-4x%2B3sqrt%283%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I feel like I can somehow turn this into a quadratic formula, but unsure how. <BR>\n" );
document.write( "So here is where I'm stuck.<BR>\n" );
document.write( "Thank you!<BR>\n" );
document.write( "-Kayte </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #251572 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=251572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x^2)sqrt(x+3)=(x+3)^(3/2)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Divide both sides by sqrt(x+3) to get:<BR>\n" );
document.write( "x^2 = (x+3)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2-x-3 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = [1 +- sqrt(1-4(-3)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = [1 +- sqrt(13)]/2<BR>\n" );
document.write( "============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );