document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=932211>Question 932211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all real solutions of the equation. Enter DNE in any empty blank.\r<BR>\n" );
document.write( "\n" );
document.write( "2x + &#8730;(x + 1)= 34<BR>\n" );
document.write( "x =   <BR>\n" );
document.write( "x =\r<BR>\n" );
document.write( "\n" );
document.write( "Please explain<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566057 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=566057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The idea is to isolate the square root and then square both sides. From there you solve for x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bsqrt%28x%2B1%29=34 ALIGN=MIDDLE  ALT=\"2x%2Bsqrt%28x%2B1%29=34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B1%29=34-2x ALIGN=MIDDLE  ALT=\"sqrt%28x%2B1%29=34-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%2B1%29%29%5E2=%2834-2x%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%2B1%29%29%5E2=%2834-2x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides (to eliminate the square root)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=%2834-2x%29%5E2 ALIGN=MIDDLE  ALT=\"x%2B1=%2834-2x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=%2834-2x%29%2834-2x%29 ALIGN=MIDDLE  ALT=\"x%2B1=%2834-2x%29%2834-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=34%2834-2x%29-2x%2834-2x%29 ALIGN=MIDDLE  ALT=\"x%2B1=34%2834-2x%29-2x%2834-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=34%2834%29%2B34%28-2x%29-2x%2834%29-2x%28-2x%29 ALIGN=MIDDLE  ALT=\"x%2B1=34%2834%29%2B34%28-2x%29-2x%2834%29-2x%28-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute again\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=1156-68x-68x%2B4x%5E2 ALIGN=MIDDLE  ALT=\"x%2B1=1156-68x-68x%2B4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=1156-68x-68x%2B4x%5E2-x-1 ALIGN=MIDDLE  ALT=\"0=1156-68x-68x%2B4x%5E2-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2-137x%2B1155 ALIGN=MIDDLE  ALT=\"0=4x%5E2-137x%2B1155\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-137x%2B1155=0 ALIGN=MIDDLE  ALT=\"4x%5E2-137x%2B1155=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now use the quadratic formula to get these two possible solutions\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+77%2F4 ALIGN=MIDDLE  ALT=\"x+=+77%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let me know if you need to see the steps to the quadratic formula (I skipped those steps to save space).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's test each possible solution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's first test <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+77%2F4 ALIGN=MIDDLE  ALT=\"x+=+77%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bsqrt%28x%2B1%29=34 ALIGN=MIDDLE  ALT=\"2x%2Bsqrt%28x%2B1%29=34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2877%2F4%29%2Bsqrt%2877%2F4%2B1%29=34 ALIGN=MIDDLE  ALT=\"2%2877%2F4%29%2Bsqrt%2877%2F4%2B1%29=34\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+77%2F4 ALIGN=MIDDLE  ALT=\"x+=+77%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43=34 ALIGN=MIDDLE  ALT=\"43=34\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That last equation above is false. This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+77%2F4 ALIGN=MIDDLE  ALT=\"x+=+77%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a true solution. It needs to satisfy the original equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and let's test <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bsqrt%28x%2B1%29=34 ALIGN=MIDDLE  ALT=\"2x%2Bsqrt%28x%2B1%29=34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2815%29%2Bsqrt%2815%2B1%29=34 ALIGN=MIDDLE  ALT=\"2%2815%29%2Bsqrt%2815%2B1%29=34\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34=34 ALIGN=MIDDLE  ALT=\"34=34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And that final equation is true. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > is indeed a true solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "===================================================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Final Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you need more one-on-one help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Alternatively, please consider visiting my website: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a> and making a donation. Any amount is greatly appreciated as it helps me a lot. This donation is to support free tutoring. Thank you.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jim\r<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------------------------------------------------------------------ </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );