document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98965>Question 98965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the solutions for the following polynomial equation. \r<BR>\n" );
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document.write( "(2x+6)^2 =36 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72052 by </B><A HREF=/tutors/aboutme.mpl?userid=doukungfoo><B>doukungfoo(195)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=doukungfoo><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=doukungfoo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=72052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem can be solved by using the quadratic formula <BR>\n" );
document.write( "which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2B-sqrt%28b%5E2-4ac%29%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2B-sqrt%28b%5E2-4ac%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "but first it needs to be be simplified to the proper format <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%5E2=36 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "first expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%5E2 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%282x%2B6%29=36 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%282x%2B6%29=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now multply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%282x%2B6%29 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%282x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the FOIL method<BR>\n" );
document.write( "so <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%282x%2B6%29=36 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%282x%2B6%29=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B12x%2B12x%2B36=36 ALIGN=MIDDLE  ALT=\"4x%5E2%2B12x%2B12x%2B36=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now simplify by combining like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x%2B36=36 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2B36=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next you want to set the equation equal to zero so that it will be in the proper format to use the quadratic formula<BR>\n" );
document.write( "So subtract 36 from both sides of the equal sign<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x%2B36-36=36-36 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2B36-36=36-36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x%2B0=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2B0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > compare it to this:<BR>\n" );
document.write( "<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;\" > you can see that the a is represented by the number 4<BR>\n" );
document.write( "the b is the number 24 and c is the number zero.<BR>\n" );
document.write( "Now you are ready to use the quadratic formula to solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2B-sqrt%28b%5E2-4ac%29%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2B-sqrt%28b%5E2-4ac%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Just replace a,b, and c with the correct number. In this problem a=4, b=24, and c=0 so now the formula looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-24%2B-sqrt%2824%5E2-4%284%29%280%29%29%2F2%284%29 ALIGN=MIDDLE  ALT=\"x=-24%2B-sqrt%2824%5E2-4%284%29%280%29%29%2F2%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "next just do the math, remembering to follow order of operations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-24%2B-sqrt%28576%29%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28-24%2B-sqrt%28576%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "At this point you need to split the equation into two seperate equations. This is done because of the +- This is how we get two answers when solving for x.<BR>\n" );
document.write( "So now we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-24%2Bsqrt%28576%29%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28-24%2Bsqrt%28576%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-24-sqrt%28576%29%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28-24-sqrt%28576%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The squareroot of 576 is 24 so now we have this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-24%2B24%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28-24%2B24%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-24-24%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28-24-24%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%280%29%2F8 ALIGN=MIDDLE  ALT=\"x=%280%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >      and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-48%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28-48%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >          and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "So finally we get our answers and remember with a quadratic equation you should always get two answers. To check them just plug them back in to the original problem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%5E2=36 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );