document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=359998>Question 359998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm reviewing for a test and I'm having serious problems with radicals. I've<BR>\n" );
document.write( "shown my progress thus far, which may or may not be correct.\r<BR>\n" );
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document.write( "sqrt(15x + 4) = 4 - sqrt(2x + 3)\r<BR>\n" );
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document.write( "square both sides:\r<BR>\n" );
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document.write( "15x + 4 = 16 - 8sqrt(2x + 3) + 2x + 3\r<BR>\n" );
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document.write( "simplify and gather like terms, then square both sides again (?)\r<BR>\n" );
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document.write( "(13x - 15)^2 = (-8sqrt(2x + 3)^2\r<BR>\n" );
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document.write( "The teacher gave us the answer of 11/169 and when finishing the problem like this, my answer was far off. Could you please walk me through this problem so I understand the steps? Thank you so much for your help :-) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256865 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=256865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sqrt(15x + 4) = 4 - sqrt(2x + 3)<BR>\n" );
document.write( "15x+4=-8sqrt(2x+3)+2x+19<BR>\n" );
document.write( "13x-15=-8sqrt(2x+3)<BR>\n" );
document.write( "You should have finished the problem; you were correct so far.<BR>\n" );
document.write( "169x^2-390x+225=128x+192<BR>\n" );
document.write( "169x^2-518x+33=0<BR>\n" );
document.write( "x=11/169 is the only answer to this problem.Quadratic equation.(see below)<BR>\n" );
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document.write( "Ed<BR>\n" );
document.write( ".<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <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;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169x%5E2%2B-518x%2B33+=+0 ALIGN=MIDDLE  ALT=\"169x%5E2%2B-518x%2B33+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-518%29%5E2-4%2A169%2A33=246016 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-518%29%5E2-4%2A169%2A33=246016\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=246016 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--518%2B-sqrt%28+246016+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--518%2B-sqrt%28+246016+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-518%29%2Bsqrt%28+246016+%29%29%2F2%5C169+=+3 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-518%29%2Bsqrt%28+246016+%29%29%2F2%5C169+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-518%29-sqrt%28+246016+%29%29%2F2%5C169+=+0.0650887573964497 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-518%29-sqrt%28+246016+%29%29%2F2%5C169+=+0.0650887573964497\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169x%5E2%2B-518x%2B33 ALIGN=MIDDLE  ALT=\"169x%5E2%2B-518x%2B33\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169x%5E2%2B-518x%2B33+=+169%28x-3%29%2A%28x-0.0650887573964497%29 ALIGN=MIDDLE  ALT=\"169x%5E2%2B-518x%2B33+=+169%28x-3%29%2A%28x-0.0650887573964497%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3, 0.0650887573964497.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+169%2Ax%5E2%2B-518%2Ax%2B33+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+169%2Ax%5E2%2B-518%2Ax%2B33+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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