document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263760>Question 263760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -/ = sqrt\r<BR>\n" );
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document.write( "1. 7+ -/(2x - 1) = 10\r<BR>\n" );
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document.write( "2.4(x - 9)^1/3 =8    \r<BR>\n" );
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document.write( "3. -/(2x - 1) = x - 8    \r<BR>\n" );
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document.write( "4. (4x + 3)^2/3 = (16x + 44)^1/3\r<BR>\n" );
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document.write( "5.   A circular table is to be made that will have a top covered with material that costs $3.50 per square foot. The covering is to cost no more than $60. What is the maximum radius for the top of the table?  (1 point) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194346 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -/ = sqrt\r<BR>\n" );
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document.write( "1. 7+ -/(2x - 1) = 10<BR>\n" );
document.write( "Multiply everything by (2x-1)<BR>\n" );
document.write( "7(2x-1)+(2x-1)=10(2x-1)<BR>\n" );
document.write( "14x-7+2x-1=20x-10<BR>\n" );
document.write( "16x-8=20x-10<BR>\n" );
document.write( "-8=4x-10<BR>\n" );
document.write( "2=4x<BR>\n" );
document.write( "1/2=x\r<BR>\n" );
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document.write( "3. -/(2x - 1) = x - 8 <BR>\n" );
document.write( " Multiply everything by (2x-1)<BR>\n" );
document.write( "(2x-1)=(x-8)(2x-1)<BR>\n" );
document.write( "2x-1=2x^2 -17x -9<BR>\n" );
document.write( "0=2x^2 -19x -8<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=2x%5E2%2B-19x%2B-8+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-19x%2B-8+=+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=%28-19%29%5E2-4%2A2%2A-8=425 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-19%29%5E2-4%2A2%2A-8=425\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=425 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--19%2B-sqrt%28+425+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--19%2B-sqrt%28+425+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+425+%29%29%2F2%5C2+=+9.90388203202208 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+425+%29%29%2F2%5C2+=+9.90388203202208\"   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-%28-19%29-sqrt%28+425+%29%29%2F2%5C2+=+-0.403882032022076 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-19%29-sqrt%28+425+%29%29%2F2%5C2+=+-0.403882032022076\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-19x%2B-8 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-19x%2B-8\"   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=2x%5E2%2B-19x%2B-8+=+2%28x-9.90388203202208%29%2A%28x--0.403882032022076%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-19x%2B-8+=+2%28x-9.90388203202208%29%2A%28x--0.403882032022076%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9.90388203202208, -0.403882032022076.\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+2%2Ax%5E2%2B-19%2Ax%2B-8+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-19%2Ax%2B-8+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "  </SPAN>\n" );
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