document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78525>Question 78525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the equations. Be sure to check your solutions.\r<BR>\n" );
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document.write( " &#8730;2y + 7+ 4=y<BR>\n" );
document.write( "(The radical symbol is over the 2y+7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56307 by </B><A HREF=/tutors/aboutme.mpl?userid=tutor_paul><B>tutor_paul(519)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutor_paul><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=tutor_paul><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=56307\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282%2Ay%29%2B7%29%2B4=y ALIGN=MIDDLE  ALT=\"sqrt%28%282%2Ay%29%2B7%29%2B4=y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First, get the terms under the radical on one side of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282%2Ay%29%2B7%29=y-4 ALIGN=MIDDLE  ALT=\"sqrt%28%282%2Ay%29%2B7%29=y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, square both sides of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ay%29%2B7=%28y-4%29%5E2 ALIGN=MIDDLE  ALT=\"%282%2Ay%29%2B7=%28y-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify, and put the equation into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ay%29%2B7=y%5E2-%288%2Ay%29%2B16 ALIGN=MIDDLE  ALT=\"%282%2Ay%29%2B7=y%5E2-%288%2Ay%29%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-%2810%2Ay%29%2B9=0 ALIGN=MIDDLE  ALT=\"y%5E2-%2810%2Ay%29%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor this expression as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-1%29%2A%28y-9%29=0 ALIGN=MIDDLE  ALT=\"%28y-1%29%2A%28y-9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that this is a second order equation, so there are two roots.<BR>\n" );
document.write( "Equate each of the factors you just found to zero and solve for y.<BR>\n" );
document.write( "You get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9 ALIGN=MIDDLE  ALT=\"y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, this part is important... you need to plug these answers<BR>\n" );
document.write( "back in to the original problem to be sure they are not \"extraneous.\"<BR>\n" );
document.write( "An extraneous root is mathematically corrrect, but not a true answer.\r<BR>\n" );
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document.write( "If you plug y=1 back into the original equation, you will see that the<BR>\n" );
document.write( "equation does NOT hold. Hence this is an extraneous root.\r<BR>\n" );
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document.write( "If you plug y=9 back into the original equation, you will see that the<BR>\n" );
document.write( "equation DOES hold. so that one is your answer. </SPAN>\n" );
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