document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=186671>Question 186671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve, step by step  &#8730;(x+5)+&#8730;(2x+3)=9\r<BR>\n" );
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document.write( "&#8730;=square root<BR>\n" );
document.write( "( )=what is under the square roots </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139936 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=139936\">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%28x%2B5%29%2Bsqrt%282x%2B3%29=9 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B5%29%2Bsqrt%282x%2B3%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B5%29=9-sqrt%282x%2B3%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B5%29=9-sqrt%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x%2B3%29 ALIGN=MIDDLE  ALT=\"sqrt%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=%289-sqrt%282x%2B3%29%29%5E2 ALIGN=MIDDLE  ALT=\"x%2B5=%289-sqrt%282x%2B3%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=81-18%2Asqrt%282x%2B3%29%2B2x%2B3 ALIGN=MIDDLE  ALT=\"x%2B5=81-18%2Asqrt%282x%2B3%29%2B2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=84%2B2x-18%2Asqrt%282x%2B3%29 ALIGN=MIDDLE  ALT=\"x%2B5=84%2B2x-18%2Asqrt%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5-84-2x=-18%2Asqrt%282x%2B3%29 ALIGN=MIDDLE  ALT=\"x%2B5-84-2x=-18%2Asqrt%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 84 from both sides. Subtract 2x from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-79=-18%2Asqrt%282x%2B3%29 ALIGN=MIDDLE  ALT=\"-x-79=-18%2Asqrt%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x-79%29%5E2=%28-18%2Asqrt%282x%2B3%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28-x-79%29%5E2=%28-18%2Asqrt%282x%2B3%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B158x%2B6241=324%2A%282x%2B3%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B158x%2B6241=324%2A%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL and square the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B158x%2B6241=648x%2B972 ALIGN=MIDDLE  ALT=\"x%5E2%2B158x%2B6241=648x%2B972\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B158x%2B6241-648x-972=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B158x%2B6241-648x-972=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything to the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-490x%2B5269=0 ALIGN=MIDDLE  ALT=\"x%5E2-490x%2B5269=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-490 ALIGN=MIDDLE  ALT=\"b=-490\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5269 ALIGN=MIDDLE  ALT=\"c=5269\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-490%29+%2B-+sqrt%28+%28-490%29%5E2-4%281%29%285269%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-490%29+%2B-+sqrt%28+%28-490%29%5E2-4%281%29%285269%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-490 ALIGN=MIDDLE  ALT=\"b=-490\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5269 ALIGN=MIDDLE  ALT=\"c=5269\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28490+%2B-+sqrt%28+%28-490%29%5E2-4%281%29%285269%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28490+%2B-+sqrt%28+%28-490%29%5E2-4%281%29%285269%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-490 ALIGN=MIDDLE  ALT=\"-490\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=490 ALIGN=MIDDLE  ALT=\"490\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28490+%2B-+sqrt%28+240100-4%281%29%285269%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28490+%2B-+sqrt%28+240100-4%281%29%285269%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-490 ALIGN=MIDDLE  ALT=\"-490\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240100 ALIGN=MIDDLE  ALT=\"240100\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28490+%2B-+sqrt%28+240100-21076+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28490+%2B-+sqrt%28+240100-21076+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%29%285269%29 ALIGN=MIDDLE  ALT=\"4%281%29%285269%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21076 ALIGN=MIDDLE  ALT=\"21076\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28490+%2B-+sqrt%28+219024+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28490+%2B-+sqrt%28+219024+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21076 ALIGN=MIDDLE  ALT=\"21076\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240100 ALIGN=MIDDLE  ALT=\"240100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=219024 ALIGN=MIDDLE  ALT=\"219024\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28490+%2B-+sqrt%28+219024+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28490+%2B-+sqrt%28+219024+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28490+%2B-+468%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28490+%2B-+468%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=219024 ALIGN=MIDDLE  ALT=\"219024\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=468 ALIGN=MIDDLE  ALT=\"468\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28490+%2B+468%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28490+%2B+468%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28490+-+468%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28490+-+468%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28958%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28958%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%2822%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=++%2822%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+479 ALIGN=MIDDLE  ALT=\"x+=+479\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11 ALIGN=MIDDLE  ALT=\"x+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the possible answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+479 ALIGN=MIDDLE  ALT=\"x+=+479\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11 ALIGN=MIDDLE  ALT=\"x+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, if you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+479 ALIGN=MIDDLE  ALT=\"x+=+479\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the original equation will NOT be true. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+479 ALIGN=MIDDLE  ALT=\"x+=+479\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a solution\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11 ALIGN=MIDDLE  ALT=\"x+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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