document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165055>Question 165055</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh>Elementary and Intermediate</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 96.) Find all real or imaginary solutions. use the method of your choice.\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt(7x+29=x+3)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121733 by </B><A HREF=/tutors/aboutme.mpl?userid=midwood_trail><B>midwood_trail(310)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=midwood_trail><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=121733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sqrt{7x + 29} = x+3 <BR>\n" );
document.write( "There is nothing to move over as the radical symbol is isolated already. <BR>\n" );
document.write( "We square both sides: <BR>\n" );
document.write( "(sqrt{7x + 29})^2 = (x+3)^2 <BR>\n" );
document.write( "7x + 29 = (x+3) (x+3) <BR>\n" );
document.write( "7x + 29 = x^2 + 6x + 9 <BR>\n" );
document.write( "Bring the entire left side to the right side and set entire equation to = 0. <BR>\n" );
document.write( "x^2 + 6x + 9 - 7x - 29 = 0 <BR>\n" );
document.write( "We now combine like terms. <BR>\n" );
document.write( "x^2 - x - 20 = 0 <BR>\n" );
document.write( "We factor this quadratic equation. <BR>\n" );
document.write( "(x + 4) (x - 5) = 0 <BR>\n" );
document.write( "Set each factor to = 0 and solve for x. <BR>\n" );
document.write( "x + 4 = 0 <BR>\n" );
document.write( "x = -4 <BR>\n" );
document.write( "====== <BR>\n" );
document.write( "x - 5 = 0 <BR>\n" );
document.write( "x = 5 <BR>\n" );
document.write( "====== \r<BR>\n" );
document.write( "\n" );
document.write( "We have two answers for x: x = -4 and x = 5 but are they both acceptable \r<BR>\n" );
document.write( "\n" );
document.write( "answers? In other words, if we replace x in the original equation with -4 and <BR>\n" );
document.write( "5, will the answer be the same on both sides of the equation? <BR>\n" );
document.write( "The only way to know is by CHECKING. \r<BR>\n" );
document.write( "\n" );
document.write( "CHECKING:\r<BR>\n" );
document.write( "\n" );
document.write( "Let x = - 4.\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt{7x + 29} = x + 3....origiginal question\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt{7(-4) + 29} = (-4) + 3\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt{-28 + 29} = -1\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt{1} = -1\r<BR>\n" );
document.write( "\n" );
document.write( "1 DOES NOT EQUAL -1.\r<BR>\n" );
document.write( "\n" );
document.write( "We REJECT x = -4 because it is does not produce the same answer on both sides of the equation after checking.\r<BR>\n" );
document.write( "\n" );
document.write( "Now, let x = 5 and do the same thing.\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt{7x + 29} = x + 3....original question\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt{7(5) + 29} = 5 + 3\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt{35 + 29} = 8\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt{64} = 8\r<BR>\n" );
document.write( "\n" );
document.write( "8 = 8...It checks!!\r<BR>\n" );
document.write( "\n" );
document.write( "The only TRUE answer here is x = 8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );