document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280963>Question 280963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been trying to figure out these equations all weekend and am having a problem trying to not only solve these problems, but also the correct way to do them.  I would appreciate any and all help in order to complete this assignment for the university.  It says there are 6 steps involved in the proper formatting of these questions involving moving the constant term to the right side of the equation, multiplying each term by 4 times the coefficient of the x squared term, squaring the coefficient of the original x term, taking the square root of both sides, and then setting the left side of the equation equal to the positive square root of the number on the right side and then setting the left side of the equation equal to the negative square root of the number on the right side.  I am completely lost and am hoping that if I give you the four problems, that you may be able to show me how each one is completed.  Thank you very much.\r<BR>\n" );
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document.write( "(1) xsquared-2x-13=0<BR>\n" );
document.write( "(2) 4xsquared-4x+3=0<BR>\n" );
document.write( "(3) xsquared+12x-64=0<BR>\n" );
document.write( "(4) 2xsquared-3x-5=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204169 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=204169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Stanborn was very generous in helping you.<BR>\n" );
document.write( "Some website rules to remember<BR>\n" );
document.write( "One problem per submission<BR>\n" );
document.write( "NO similar problems<BR>\n" );
document.write( "limit 4 submissions daily<BR>\n" );
document.write( "squared is written ^2<BR>\n" );
document.write( "cubed  ^3<BR>\n" );
document.write( "x^2-2x-13=0<BR>\n" );
document.write( "There are three common ways to solve quadratic equations<BR>\n" );
document.write( "1-factor<BR>\n" );
document.write( "2-complete the square<BR>\n" );
document.write( "3-quadratic formula<BR>\n" );
document.write( "This one can't be factored<BR>\n" );
document.write( "You can use complete the square.<BR>\n" );
document.write( "SOME of your 6 steps look like it might be an attempt to complete the square.\r<BR>\n" );
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document.write( "x^2-2x-13=0<BR>\n" );
document.write( "get the constant on the right<BR>\n" );
document.write( "x^2-2x=13<BR>\n" );
document.write( "the coeficient of x^2 must be one. It is.<BR>\n" );
document.write( "take the coefficient of x not x^2<BR>\n" );
document.write( "-2<BR>\n" );
document.write( "take half<BR>\n" );
document.write( "-2/2<BR>\n" );
document.write( "square it<BR>\n" );
document.write( " 1<BR>\n" );
document.write( "add it to both sides<BR>\n" );
document.write( "x^2-2x+1=14<BR>\n" );
document.write( "(x-1)^2=14<BR>\n" );
document.write( "take square root<BR>\n" );
document.write( "x-1=sqrt(14)<BR>\n" );
document.write( "x-1=-sqrt(14)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Bsqrt%2814%29 ALIGN=MIDDLE  ALT=\"x=1%2Bsqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1-sqrt%2814%29 ALIGN=MIDDLE  ALT=\"x=1-sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "see below for approximate values\r<BR>\n" );
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document.write( "Quadratic formula works on ALL quadratic equations.<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=1x%5E2%2B-2x%2B-13+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-13+=+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=%28-2%29%5E2-4%2A1%2A-13=56 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-13=56\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=56 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--2%2B-sqrt%28+56+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2%2B-sqrt%28+56+%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-%28-2%29%2Bsqrt%28+56+%29%29%2F2%5C1+=+4.74165738677394 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+56+%29%29%2F2%5C1+=+4.74165738677394\"   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-%28-2%29-sqrt%28+56+%29%29%2F2%5C1+=+-2.74165738677394 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-2%29-sqrt%28+56+%29%29%2F2%5C1+=+-2.74165738677394\"   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=1x%5E2%2B-2x%2B-13 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-13\"   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=1x%5E2%2B-2x%2B-13+=+1%28x-4.74165738677394%29%2A%28x--2.74165738677394%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-13+=+1%28x-4.74165738677394%29%2A%28x--2.74165738677394%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4.74165738677394, -2.74165738677394.\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+1%2Ax%5E2%2B-2%2Ax%2B-13+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-13+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );