document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143984>Question 143984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you so much for your help!  Can you please help me solve the equation....\r<BR>\n" );
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document.write( "42x + 4x+1 – 6 = 0\r<BR>\n" );
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document.write( "(the exponents are the 2x and x+1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104812 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=104812\">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=4%5E%282x%29%2B4%5E%28x%2B1%29-6=0 ALIGN=MIDDLE  ALT=\"4%5E%282x%29%2B4%5E%28x%2B1%29-6=0\"   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=4%5E%282x%29%2B4%5E%28x%29%2A4%5E%281%29-6=0 ALIGN=MIDDLE  ALT=\"4%5E%282x%29%2B4%5E%28x%29%2A4%5E%281%29-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%28x%2B1%29 ALIGN=MIDDLE  ALT=\"4%5E%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%28x%29%2A4%5E%281%29 ALIGN=MIDDLE  ALT=\"4%5E%28x%29%2A4%5E%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28y%2Bz%29=x%5E%28y%29%2Ax%5E%28z%29 ALIGN=MIDDLE  ALT=\"x%5E%28y%2Bz%29=x%5E%28y%29%2Ax%5E%28z%29\"   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=4%5E%282x%29%2B4%5E%28x%29%2A4-6=0 ALIGN=MIDDLE  ALT=\"4%5E%282x%29%2B4%5E%28x%29%2A4-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E1 ALIGN=MIDDLE  ALT=\"4%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%282x%29%2B4%2A4%5E%28x%29-6=0 ALIGN=MIDDLE  ALT=\"4%5E%282x%29%2B4%2A4%5E%28x%29-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E%28x%29%29%5E2%2B4%2A4%5E%28x%29-6=0 ALIGN=MIDDLE  ALT=\"%284%5E%28x%29%29%5E2%2B4%2A4%5E%28x%29-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%282x%29 ALIGN=MIDDLE  ALT=\"4%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%284%5E%28x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28y%2Az%29=%28x%5E%28y%29%29%5Ez ALIGN=MIDDLE  ALT=\"x%5E%28y%2Az%29=%28x%5E%28y%29%29%5Ez\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=4%5Ex ALIGN=MIDDLE  ALT=\"u=4%5Ex\"   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=u%5E2%2B4%2Au-6=0 ALIGN=MIDDLE  ALT=\"u%5E2%2B4%2Au-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=4%5Ex ALIGN=MIDDLE  ALT=\"u=4%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each instance of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex ALIGN=MIDDLE  ALT=\"4%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > with \"u\"\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"u\":\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2%2B4%2Au-6=0 ALIGN=MIDDLE  ALT=\"u%5E2%2B4%2Au-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-6 ALIGN=MIDDLE  ALT=\"c=-6\"   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=u+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"u+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=4, and c=-6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A-6+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"u+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A-6+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 4 to get 16  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-4+%2B-+sqrt%28+16%2B24+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"u+=+%28-4+%2B-+sqrt%28+16%2B24+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-6%2A1 ALIGN=MIDDLE  ALT=\"-4%2A-6%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   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=u+=+%28-4+%2B-+sqrt%28+40+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"u+=+%28-4+%2B-+sqrt%28+40+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-4+%2B-+2%2Asqrt%2810%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"u+=+%28-4+%2B-+2%2Asqrt%2810%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-4+%2B-+2%2Asqrt%2810%29%29%2F2 ALIGN=MIDDLE  ALT=\"u+=+%28-4+%2B-+2%2Asqrt%2810%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-4+%2B+2%2Asqrt%2810%29%29%2F2 ALIGN=MIDDLE  ALT=\"u+=+%28-4+%2B+2%2Asqrt%2810%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-4+-+2%2Asqrt%2810%29%29%2F2 ALIGN=MIDDLE  ALT=\"u+=+%28-4+-+2%2Asqrt%2810%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-4%2F2%2B2%2Asqrt%2810%29%2F2 ALIGN=MIDDLE  ALT=\"u=-4%2F2%2B2%2Asqrt%2810%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-4%2F2-2%2Asqrt%2810%29%2F2 ALIGN=MIDDLE  ALT=\"u=-4%2F2-2%2Asqrt%2810%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-2%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"u=-2%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-2-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"u=-2-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember, we let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=4%5Ex ALIGN=MIDDLE  ALT=\"u=4%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=-2%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%5Ex=-2%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=-2-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%5Ex=-2-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's solve the first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=-2%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%5Ex=-2%2Bsqrt%2810%29\"   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=4%5Ex=-2%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%5Ex=-2%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%284%5Ex%29%29=log%2810%2C%28-2%2Bsqrt%2810%29%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%284%5Ex%29%29=log%2810%2C%28-2%2Bsqrt%2810%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%2810%2C%284%29%29=log%2810%2C%28-2%2Bsqrt%2810%29%29%29 ALIGN=MIDDLE  ALT=\"x%2Alog%2810%2C%284%29%29=log%2810%2C%28-2%2Bsqrt%2810%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the left side using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29\"   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=log%2810%2C%28-2%2Bsqrt%2810%29%29%29%2Flog%2810%2C%284%29%29 ALIGN=MIDDLE  ALT=\"x=log%2810%2C%28-2%2Bsqrt%2810%29%29%29%2Flog%2810%2C%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%284%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=log%284%2C%28-2%2Bsqrt%2810%29%29%29 ALIGN=MIDDLE  ALT=\"x=log%284%2C%28-2%2Bsqrt%2810%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the logs by use of the change of base formula\r<BR>\n" );
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document.write( "Now let's solve the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=-2-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%5Ex=-2-sqrt%2810%29\"   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=4%5Ex=-2%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%5Ex=-2%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%284%5Ex%29%29=log%2810%2C%28-2-sqrt%2810%29%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%284%5Ex%29%29=log%2810%2C%28-2-sqrt%2810%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log of both sides\r<BR>\n" );
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document.write( "Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2-sqrt%2810%29=-5.16228 ALIGN=MIDDLE  ALT=\"-2-sqrt%2810%29=-5.16228\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since we cannot take the log of a negative number, this means we must ignore it.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is \r<BR>\n" );
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document.write( "which approximates to \r<BR>\n" );
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